%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP187-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:39 AM UTC 2026
% Result : Unsatisfiable 102.81s 13.43s
% Output : CNFRefutation 105.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 15
% Syntax : Number of clauses : 755 ( 755 unt; 0 nHn; 348 RR)
% Number of literals : 755 ( 754 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 830 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,b) != multiply(b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p33) ).
cnf(c2,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c3,plain,
greatest_lower_bound(inverse(X2),identity) = greatest_lower_bound(identity,inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
greatest_lower_bound(identity,inverse(X2)) = greatest_lower_bound(inverse(X2),identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
inverse(greatest_lower_bound(identity,inverse(X2))) = inverse(greatest_lower_bound(inverse(X2),identity)),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X2))),greatest_lower_bound(X2,identity)) = multiply(inverse(greatest_lower_bound(inverse(X2),identity)),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(X2,multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(inverse(greatest_lower_bound(inverse(X2),identity)),greatest_lower_bound(X2,identity)) = multiply(inverse(greatest_lower_bound(inverse(X2),identity)),greatest_lower_bound(X2,multiply(inverse(X2),X2))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(greatest_lower_bound(X2,identity),X3) = multiply(greatest_lower_bound(identity,X2),X3),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(greatest_lower_bound(Y2,Z),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c15,plain,
multiply(greatest_lower_bound(identity,X3),X2) = greatest_lower_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c17,plain,
greatest_lower_bound(multiply(identity,X2),multiply(X3,X2)) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(greatest_lower_bound(identity,X3),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c15,c17]) ).
cnf(c19,plain,
multiply(greatest_lower_bound(X3,identity),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c13,c18]) ).
cnf(c20,plain,
greatest_lower_bound(X2,multiply(X3,X2)) = multiply(greatest_lower_bound(X3,identity),X2),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(inverse(greatest_lower_bound(X3,identity)),greatest_lower_bound(X2,multiply(X3,X2))) = multiply(inverse(greatest_lower_bound(X3,identity)),multiply(greatest_lower_bound(X3,identity),X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c23,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c7]) ).
cnf(c26,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c25,c16]) ).
cnf(c27,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
multiply(inverse(greatest_lower_bound(X3,identity)),multiply(greatest_lower_bound(X3,identity),X2)) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
multiply(inverse(greatest_lower_bound(X3,identity)),greatest_lower_bound(X2,multiply(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c21,c28]) ).
cnf(c30,plain,
multiply(inverse(greatest_lower_bound(inverse(X2),identity)),greatest_lower_bound(X2,multiply(inverse(X2),X2))) = X2,
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(inverse(greatest_lower_bound(inverse(X2),identity)),greatest_lower_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c10,c30]) ).
cnf(c32,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(X2))),greatest_lower_bound(X2,identity)) = X2,
inference(transitivity,[status(thm)],[c6,c31]) ).
cnf(c33,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(b,a)))),greatest_lower_bound(multiply(b,a),identity)) = multiply(b,a),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(b,a) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(b,a)))),greatest_lower_bound(multiply(b,a),identity)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))) = greatest_lower_bound(inverse(multiply(b,a)),multiply(multiply(a,b),inverse(multiply(b,a)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c36,plain,
greatest_lower_bound(inverse(multiply(b,a)),multiply(multiply(a,b),inverse(multiply(b,a)))) = multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
greatest_lower_bound(greatest_lower_bound(X3,X4),X2) = greatest_lower_bound(X2,greatest_lower_bound(X3,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c40,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c43,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c41,c43]) ).
cnf(c45,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c38,c44]) ).
cnf(c46,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(multiply(b,a),identity)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,b)) = greatest_lower_bound(a,greatest_lower_bound(identity,b)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c48,plain,
greatest_lower_bound(least_upper_bound(X4,X2),X3) = greatest_lower_bound(X3,least_upper_bound(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c49,plain,
greatest_lower_bound(X3,least_upper_bound(X4,X2)) = greatest_lower_bound(least_upper_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,least_upper_bound(X4,X2))) = greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),X3)),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),X3)) = greatest_lower_bound(greatest_lower_bound(X4,least_upper_bound(X4,X2)),X3),
inference(substitution,[status(thm)],[c39]) ).
cnf(c52,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c53,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c52]) ).
cnf(c54,plain,
greatest_lower_bound(greatest_lower_bound(X4,least_upper_bound(X4,X2)),X3) = greatest_lower_bound(X4,X3),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X2),X3)) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c51,c54]) ).
cnf(c56,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,least_upper_bound(X4,X2))) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c50,c55]) ).
cnf(c57,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(b,least_upper_bound(a,inverse(a))),
inference(substitution,[status(thm)],[c56]) ).
cnf(c58,plain,
greatest_lower_bound(b,least_upper_bound(a,inverse(a))) = greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,axiom,
greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b))) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c60,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(b,identity),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c62,plain,
greatest_lower_bound(b,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(identity,b),
inference(transitivity,[status(thm)],[c60,c61]) ).
cnf(c63,plain,
greatest_lower_bound(b,least_upper_bound(a,inverse(a))) = greatest_lower_bound(identity,b),
inference(transitivity,[status(thm)],[c58,c62]) ).
cnf(c64,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,least_upper_bound(a,inverse(a))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
greatest_lower_bound(a,greatest_lower_bound(identity,b)) = greatest_lower_bound(a,greatest_lower_bound(b,least_upper_bound(a,inverse(a)))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
greatest_lower_bound(a,greatest_lower_bound(b,least_upper_bound(a,inverse(a)))) = greatest_lower_bound(a,b),
inference(substitution,[status(thm)],[c56]) ).
cnf(c67,plain,
greatest_lower_bound(a,greatest_lower_bound(identity,b)) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[c65,c66]) ).
cnf(c68,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[c47,c67]) ).
cnf(c69,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(identity,greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(a,b)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,b))),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,X2)) = greatest_lower_bound(greatest_lower_bound(identity,a),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c72,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(greatest_lower_bound(identity,a),X2)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
greatest_lower_bound(X2,greatest_lower_bound(identity,a)) = greatest_lower_bound(greatest_lower_bound(identity,a),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c74,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),X2) = greatest_lower_bound(X2,greatest_lower_bound(identity,a)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(X2,greatest_lower_bound(identity,a))),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
greatest_lower_bound(X2,greatest_lower_bound(identity,a)) = greatest_lower_bound(identity,greatest_lower_bound(X2,a)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c77,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(X2,greatest_lower_bound(identity,a))) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(X2,a))),
inference(congruence,[status(thm)],[c76]) ).
cnf(c78,plain,
greatest_lower_bound(a,X2) = greatest_lower_bound(X2,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c79,plain,
greatest_lower_bound(X2,a) = greatest_lower_bound(a,X2),
inference(symmetry,[status(thm)],[c78]) ).
cnf(c80,plain,
greatest_lower_bound(identity,greatest_lower_bound(X2,a)) = greatest_lower_bound(identity,greatest_lower_bound(a,X2)),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(X2,a))) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,X2))),
inference(congruence,[status(thm)],[c80]) ).
cnf(c82,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,X2)) = greatest_lower_bound(greatest_lower_bound(identity,a),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c83,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(greatest_lower_bound(identity,a),X2)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c85,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c86,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c85]) ).
cnf(c87,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c88,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c86,c87]) ).
cnf(c89,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c88]) ).
cnf(c90,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c92,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c94,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c92,c93]) ).
cnf(c95,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c90,c94]) ).
cnf(c96,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
a = multiply(a,identity),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(identity,multiply(a,identity)),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,multiply(a,identity))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
greatest_lower_bound(inverse(X3),X2) = greatest_lower_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c101,plain,
greatest_lower_bound(X2,inverse(X3)) = greatest_lower_bound(inverse(X3),X2),
inference(symmetry,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(X3,greatest_lower_bound(X2,inverse(X3))) = multiply(X3,greatest_lower_bound(inverse(X3),X2)),
inference(congruence,[status(thm)],[c101]) ).
cnf(c103,plain,
multiply(inverse(inverse(X3)),greatest_lower_bound(inverse(X3),X2)) = multiply(X3,greatest_lower_bound(inverse(X3),X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c104,plain,
multiply(X3,greatest_lower_bound(inverse(X3),X2)) = multiply(inverse(inverse(X3)),greatest_lower_bound(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c106,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c107,plain,
greatest_lower_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c108,plain,
multiply(inverse(X3),greatest_lower_bound(X3,X2)) = greatest_lower_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
multiply(inverse(inverse(X3)),greatest_lower_bound(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(inverse(inverse(X3)),X2)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
greatest_lower_bound(identity,multiply(inverse(inverse(X3)),X2)) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c111,plain,
multiply(inverse(inverse(X3)),greatest_lower_bound(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c109,c110]) ).
cnf(c112,plain,
multiply(X3,greatest_lower_bound(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c104,c111]) ).
cnf(c113,plain,
multiply(X3,greatest_lower_bound(X2,inverse(X3))) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c102,c112]) ).
cnf(c114,plain,
multiply(a,greatest_lower_bound(identity,inverse(a))) = greatest_lower_bound(identity,multiply(a,identity)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
greatest_lower_bound(identity,multiply(a,identity)) = multiply(a,greatest_lower_bound(identity,inverse(a))),
inference(symmetry,[status(thm)],[c114]) ).
cnf(c116,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,multiply(a,identity))) = greatest_lower_bound(multiply(a,b),multiply(a,greatest_lower_bound(identity,inverse(a)))),
inference(congruence,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(X4,greatest_lower_bound(X2,greatest_lower_bound(X3,X5))) = greatest_lower_bound(multiply(X4,X2),multiply(X4,greatest_lower_bound(X3,X5))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c118,plain,
greatest_lower_bound(multiply(X5,X3),multiply(X5,greatest_lower_bound(X4,X2))) = multiply(X5,greatest_lower_bound(X3,greatest_lower_bound(X4,X2))),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,greatest_lower_bound(X4,X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c120,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,X2)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(X5,greatest_lower_bound(X3,greatest_lower_bound(X4,X2))) = multiply(X5,greatest_lower_bound(X4,greatest_lower_bound(X3,X2))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
greatest_lower_bound(multiply(X5,X3),multiply(X5,greatest_lower_bound(X4,X2))) = multiply(X5,greatest_lower_bound(X4,greatest_lower_bound(X3,X2))),
inference(transitivity,[status(thm)],[c118,c121]) ).
cnf(c123,plain,
greatest_lower_bound(multiply(a,b),multiply(a,greatest_lower_bound(identity,inverse(a)))) = multiply(a,greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a)))),
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
greatest_lower_bound(inverse(a),b) = greatest_lower_bound(b,inverse(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c125,plain,
greatest_lower_bound(b,inverse(a)) = greatest_lower_bound(inverse(a),b),
inference(symmetry,[status(thm)],[c124]) ).
cnf(c126,plain,
greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(identity,greatest_lower_bound(inverse(a),b)),
inference(congruence,[status(thm)],[c125]) ).
cnf(c127,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(a),b)) = greatest_lower_bound(inverse(a),greatest_lower_bound(identity,b)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c128,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,least_upper_bound(a,inverse(a))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c129,plain,
greatest_lower_bound(inverse(a),greatest_lower_bound(identity,b)) = greatest_lower_bound(inverse(a),greatest_lower_bound(b,least_upper_bound(a,inverse(a)))),
inference(congruence,[status(thm)],[c128]) ).
cnf(c130,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,least_upper_bound(X2,X4))) = greatest_lower_bound(X3,greatest_lower_bound(X4,least_upper_bound(X2,X4))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c131,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c132,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c52]) ).
cnf(c136,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c134,c135]) ).
cnf(c137,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,least_upper_bound(X2,X4))) = greatest_lower_bound(X3,X4),
inference(congruence,[status(thm)],[c136]) ).
cnf(c138,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c139,plain,
greatest_lower_bound(X3,greatest_lower_bound(X4,least_upper_bound(X2,X4))) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c137,c138]) ).
cnf(c140,plain,
greatest_lower_bound(X4,greatest_lower_bound(X3,least_upper_bound(X2,X4))) = greatest_lower_bound(X4,X3),
inference(transitivity,[status(thm)],[c130,c139]) ).
cnf(c141,plain,
greatest_lower_bound(inverse(a),greatest_lower_bound(b,least_upper_bound(a,inverse(a)))) = greatest_lower_bound(inverse(a),b),
inference(substitution,[status(thm)],[c140]) ).
cnf(c142,plain,
greatest_lower_bound(inverse(a),b) = greatest_lower_bound(b,inverse(a)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c143,plain,
greatest_lower_bound(inverse(a),greatest_lower_bound(b,least_upper_bound(a,inverse(a)))) = greatest_lower_bound(b,inverse(a)),
inference(transitivity,[status(thm)],[c141,c142]) ).
cnf(c144,plain,
greatest_lower_bound(inverse(a),greatest_lower_bound(identity,b)) = greatest_lower_bound(b,inverse(a)),
inference(transitivity,[status(thm)],[c129,c143]) ).
cnf(c145,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(a),b)) = greatest_lower_bound(b,inverse(a)),
inference(transitivity,[status(thm)],[c127,c144]) ).
cnf(c146,plain,
greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(b,inverse(a)),
inference(transitivity,[status(thm)],[c126,c145]) ).
cnf(c147,plain,
multiply(a,greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a)))) = multiply(a,greatest_lower_bound(b,inverse(a))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(a,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(multiply(a,b),multiply(a,inverse(a))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c149,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c150,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c7]) ).
cnf(c152,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
multiply(a,inverse(a)) = identity,
inference(substitution,[status(thm)],[c152]) ).
cnf(c154,plain,
greatest_lower_bound(multiply(a,b),multiply(a,inverse(a))) = greatest_lower_bound(multiply(a,b),identity),
inference(congruence,[status(thm)],[c153]) ).
cnf(c155,plain,
multiply(a,greatest_lower_bound(b,inverse(a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c148,c154]) ).
cnf(c156,plain,
multiply(a,greatest_lower_bound(identity,greatest_lower_bound(b,inverse(a)))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c147,c155]) ).
cnf(c157,plain,
greatest_lower_bound(multiply(a,b),multiply(a,greatest_lower_bound(identity,inverse(a)))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c123,c156]) ).
cnf(c158,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,multiply(a,identity))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c116,c157]) ).
cnf(c159,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c99,c158]) ).
cnf(c160,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)),X2) = greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),X2),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,X2)) = greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c162,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),X2) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,X2)),
inference(symmetry,[status(thm)],[c161]) ).
cnf(c163,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c164,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,X2)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c166,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(X2,identity)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c164,c166]) ).
cnf(c168,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),X2) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c162,c167]) ).
cnf(c169,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,a)),X2) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c160,c168]) ).
cnf(c170,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c84,c169]) ).
cnf(c171,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c83,c170]) ).
cnf(c172,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(X2,a))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c81,c171]) ).
cnf(c173,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(X2,greatest_lower_bound(identity,a))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c77,c172]) ).
cnf(c174,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c75,c173]) ).
cnf(c175,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(transitivity,[status(thm)],[c72,c174]) ).
cnf(c176,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,b))) = greatest_lower_bound(b,greatest_lower_bound(multiply(a,b),identity)),
inference(substitution,[status(thm)],[c175]) ).
cnf(c177,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,identity)) = greatest_lower_bound(b,greatest_lower_bound(multiply(a,b),identity)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c178,plain,
greatest_lower_bound(b,greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,identity)),
inference(symmetry,[status(thm)],[c177]) ).
cnf(c179,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c180,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,identity)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,b)),
inference(congruence,[status(thm)],[c179]) ).
cnf(c181,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),b)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c182,plain,
least_upper_bound(inverse(X2),X3) = least_upper_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c183,plain,
least_upper_bound(X3,inverse(X2)) = least_upper_bound(inverse(X2),X3),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
multiply(least_upper_bound(X3,inverse(X2)),X2) = multiply(least_upper_bound(inverse(X2),X3),X2),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c186,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
least_upper_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = least_upper_bound(identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c188,plain,
multiply(least_upper_bound(inverse(X2),X3),X2) = least_upper_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c186,c187]) ).
cnf(c189,plain,
multiply(least_upper_bound(X3,inverse(X2)),X2) = least_upper_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c184,c188]) ).
cnf(c190,plain,
multiply(least_upper_bound(b,inverse(b)),b) = least_upper_bound(identity,multiply(b,b)),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
least_upper_bound(identity,multiply(b,b)) = multiply(least_upper_bound(b,inverse(b)),b),
inference(symmetry,[status(thm)],[c190]) ).
cnf(c192,plain,
greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(b,b))) = greatest_lower_bound(multiply(a,b),multiply(least_upper_bound(b,inverse(b)),b)),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(greatest_lower_bound(a,least_upper_bound(b,inverse(b))),b) = greatest_lower_bound(multiply(a,b),multiply(least_upper_bound(b,inverse(b)),b)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c194,plain,
greatest_lower_bound(multiply(a,b),multiply(least_upper_bound(b,inverse(b)),b)) = multiply(greatest_lower_bound(a,least_upper_bound(b,inverse(b))),b),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
greatest_lower_bound(X2,least_upper_bound(X4,X3)) = greatest_lower_bound(least_upper_bound(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c196,plain,
greatest_lower_bound(least_upper_bound(X4,X3),X2) = greatest_lower_bound(X2,least_upper_bound(X4,X3)),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),X2)) = greatest_lower_bound(X4,greatest_lower_bound(X2,least_upper_bound(X4,X3))),
inference(congruence,[status(thm)],[c196]) ).
cnf(c198,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,least_upper_bound(X4,X3))) = greatest_lower_bound(X4,X2),
inference(substitution,[status(thm)],[c56]) ).
cnf(c199,plain,
greatest_lower_bound(X4,greatest_lower_bound(least_upper_bound(X4,X3),X2)) = greatest_lower_bound(X4,X2),
inference(transitivity,[status(thm)],[c197,c198]) ).
cnf(c200,plain,
greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(a,least_upper_bound(b,inverse(b))),
inference(substitution,[status(thm)],[c199]) ).
cnf(c201,plain,
greatest_lower_bound(a,least_upper_bound(b,inverse(b))) = greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))),
inference(symmetry,[status(thm)],[c200]) ).
cnf(c202,plain,
greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(a,identity),
inference(congruence,[status(thm)],[c59]) ).
cnf(c203,plain,
greatest_lower_bound(a,identity) = greatest_lower_bound(identity,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c204,plain,
greatest_lower_bound(a,greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c202,c203]) ).
cnf(c205,plain,
greatest_lower_bound(a,least_upper_bound(b,inverse(b))) = greatest_lower_bound(identity,a),
inference(transitivity,[status(thm)],[c201,c204]) ).
cnf(c206,plain,
multiply(greatest_lower_bound(a,least_upper_bound(b,inverse(b))),b) = multiply(greatest_lower_bound(identity,a),b),
inference(congruence,[status(thm)],[c205]) ).
cnf(c207,plain,
multiply(greatest_lower_bound(X3,X4),X2) = greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c208,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c207]) ).
cnf(c209,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c210,plain,
multiply(greatest_lower_bound(X3,X4),X2) = multiply(greatest_lower_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c208,c210]) ).
cnf(c212,plain,
greatest_lower_bound(multiply(a,b),multiply(identity,b)) = multiply(greatest_lower_bound(identity,a),b),
inference(substitution,[status(thm)],[c211]) ).
cnf(c213,plain,
multiply(greatest_lower_bound(identity,a),b) = greatest_lower_bound(multiply(a,b),multiply(identity,b)),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c214,plain,
multiply(identity,b) = b,
inference(substitution,[status(thm)],[c16]) ).
cnf(c215,plain,
greatest_lower_bound(multiply(a,b),multiply(identity,b)) = greatest_lower_bound(multiply(a,b),b),
inference(congruence,[status(thm)],[c214]) ).
cnf(c216,plain,
multiply(greatest_lower_bound(identity,a),b) = greatest_lower_bound(multiply(a,b),b),
inference(transitivity,[status(thm)],[c213,c215]) ).
cnf(c217,plain,
multiply(greatest_lower_bound(a,least_upper_bound(b,inverse(b))),b) = greatest_lower_bound(multiply(a,b),b),
inference(transitivity,[status(thm)],[c206,c216]) ).
cnf(c218,plain,
greatest_lower_bound(multiply(a,b),multiply(least_upper_bound(b,inverse(b)),b)) = greatest_lower_bound(multiply(a,b),b),
inference(transitivity,[status(thm)],[c194,c217]) ).
cnf(c219,plain,
greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(b,b))) = greatest_lower_bound(multiply(a,b),b),
inference(transitivity,[status(thm)],[c192,c218]) ).
cnf(c220,plain,
greatest_lower_bound(multiply(a,b),b) = greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(b,b))),
inference(symmetry,[status(thm)],[c219]) ).
cnf(c221,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(b,b)))),
inference(congruence,[status(thm)],[c220]) ).
cnf(c222,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(b,b)))) = greatest_lower_bound(identity,multiply(a,b)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c223,plain,
greatest_lower_bound(identity,multiply(a,b)) = greatest_lower_bound(multiply(a,b),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c224,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),least_upper_bound(identity,multiply(b,b)))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c222,c223]) ).
cnf(c225,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(a,b),b)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c221,c224]) ).
cnf(c226,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,b)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c181,c225]) ).
cnf(c227,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(b,identity)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c180,c226]) ).
cnf(c228,plain,
greatest_lower_bound(b,greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c178,c227]) ).
cnf(c229,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,greatest_lower_bound(a,b))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c176,c228]) ).
cnf(c230,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(a,b)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c70,c229]) ).
cnf(c231,plain,
greatest_lower_bound(multiply(a,b),identity) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(a,b)) = greatest_lower_bound(a,greatest_lower_bound(multiply(a,b),b)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c233,plain,
greatest_lower_bound(b,multiply(a,b)) = greatest_lower_bound(multiply(a,b),b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c234,plain,
greatest_lower_bound(multiply(a,b),b) = greatest_lower_bound(b,multiply(a,b)),
inference(symmetry,[status(thm)],[c233]) ).
cnf(c235,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(a,b),b)) = greatest_lower_bound(a,greatest_lower_bound(b,multiply(a,b))),
inference(congruence,[status(thm)],[c234]) ).
cnf(c236,plain,
greatest_lower_bound(a,greatest_lower_bound(b,multiply(a,b))) = greatest_lower_bound(greatest_lower_bound(a,b),multiply(a,b)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c237,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c238,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(b,a),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(a,b)) = least_upper_bound(multiply(a,b),greatest_lower_bound(b,a)),
inference(congruence,[status(thm)],[c238]) ).
cnf(c240,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c95]) ).
cnf(c241,plain,
a = multiply(a,identity),
inference(symmetry,[status(thm)],[c240]) ).
cnf(c242,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(b,multiply(a,identity)),
inference(congruence,[status(thm)],[c241]) ).
cnf(c243,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(b,a)) = least_upper_bound(multiply(a,b),greatest_lower_bound(b,multiply(a,identity))),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(inverse(inverse(X4)),greatest_lower_bound(X3,multiply(inverse(X4),X2))) = multiply(X4,greatest_lower_bound(X3,multiply(inverse(X4),X2))),
inference(substitution,[status(thm)],[c88]) ).
cnf(c245,plain,
multiply(X4,greatest_lower_bound(X3,multiply(inverse(X4),X2))) = multiply(inverse(inverse(X4)),greatest_lower_bound(X3,multiply(inverse(X4),X2))),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
greatest_lower_bound(multiply(X4,X2),X3) = greatest_lower_bound(X3,multiply(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c247,plain,
greatest_lower_bound(X3,multiply(X4,X2)) = greatest_lower_bound(multiply(X4,X2),X3),
inference(symmetry,[status(thm)],[c246]) ).
cnf(c248,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(X4,X2))) = multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)),
inference(congruence,[status(thm)],[c247]) ).
cnf(c249,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)) = greatest_lower_bound(multiply(inverse(X4),multiply(X4,X2)),multiply(inverse(X4),X3)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c250,plain,
greatest_lower_bound(multiply(inverse(X4),multiply(X4,X2)),multiply(inverse(X4),X3)) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c251,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X2),X3)) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c249,c250]) ).
cnf(c252,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(X4,X2))) = greatest_lower_bound(X2,multiply(inverse(X4),X3)),
inference(transitivity,[status(thm)],[c248,c251]) ).
cnf(c253,plain,
multiply(inverse(X4),greatest_lower_bound(X2,multiply(X4,X3))) = greatest_lower_bound(X3,multiply(inverse(X4),X2)),
inference(substitution,[status(thm)],[c252]) ).
cnf(c254,plain,
greatest_lower_bound(X3,multiply(inverse(X4),X2)) = multiply(inverse(X4),greatest_lower_bound(X2,multiply(X4,X3))),
inference(symmetry,[status(thm)],[c253]) ).
cnf(c255,plain,
multiply(inverse(inverse(X4)),greatest_lower_bound(X3,multiply(inverse(X4),X2))) = multiply(inverse(inverse(X4)),multiply(inverse(X4),greatest_lower_bound(X2,multiply(X4,X3)))),
inference(congruence,[status(thm)],[c254]) ).
cnf(c256,plain,
multiply(inverse(inverse(X4)),multiply(inverse(X4),greatest_lower_bound(X2,multiply(X4,X3)))) = greatest_lower_bound(X2,multiply(X4,X3)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c257,plain,
multiply(inverse(inverse(X4)),greatest_lower_bound(X3,multiply(inverse(X4),X2))) = greatest_lower_bound(X2,multiply(X4,X3)),
inference(transitivity,[status(thm)],[c255,c256]) ).
cnf(c258,plain,
multiply(X4,greatest_lower_bound(X3,multiply(inverse(X4),X2))) = greatest_lower_bound(X2,multiply(X4,X3)),
inference(transitivity,[status(thm)],[c245,c257]) ).
cnf(c259,plain,
multiply(a,greatest_lower_bound(identity,multiply(inverse(a),b))) = greatest_lower_bound(b,multiply(a,identity)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c260,plain,
greatest_lower_bound(b,multiply(a,identity)) = multiply(a,greatest_lower_bound(identity,multiply(inverse(a),b))),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(b,multiply(a,identity))) = least_upper_bound(multiply(a,b),multiply(a,greatest_lower_bound(identity,multiply(inverse(a),b)))),
inference(congruence,[status(thm)],[c260]) ).
cnf(c262,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c263,plain,
multiply(a,least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b)))) = least_upper_bound(multiply(a,b),multiply(a,greatest_lower_bound(identity,multiply(inverse(a),b)))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c264,plain,
least_upper_bound(multiply(a,b),multiply(a,greatest_lower_bound(identity,multiply(inverse(a),b)))) = multiply(a,least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b)))),
inference(symmetry,[status(thm)],[c263]) ).
cnf(c265,plain,
least_upper_bound(greatest_lower_bound(X3,inverse(X2)),identity) = least_upper_bound(identity,greatest_lower_bound(X3,inverse(X2))),
inference(substitution,[status(thm)],[c131]) ).
cnf(c266,plain,
least_upper_bound(identity,greatest_lower_bound(X3,inverse(X2))) = least_upper_bound(greatest_lower_bound(X3,inverse(X2)),identity),
inference(symmetry,[status(thm)],[c265]) ).
cnf(c267,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X3,inverse(X2))),X2) = multiply(least_upper_bound(greatest_lower_bound(X3,inverse(X2)),identity),X2),
inference(congruence,[status(thm)],[c266]) ).
cnf(c268,plain,
least_upper_bound(identity,X2) = least_upper_bound(X2,identity),
inference(substitution,[status(thm)],[c131]) ).
cnf(c269,plain,
least_upper_bound(X2,identity) = least_upper_bound(identity,X2),
inference(symmetry,[status(thm)],[c268]) ).
cnf(c270,plain,
multiply(least_upper_bound(X3,identity),X2) = multiply(least_upper_bound(identity,X3),X2),
inference(congruence,[status(thm)],[c269]) ).
cnf(c271,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c272,plain,
least_upper_bound(multiply(identity,X2),multiply(X3,X2)) = least_upper_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c273,plain,
multiply(least_upper_bound(identity,X3),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c271,c272]) ).
cnf(c274,plain,
multiply(least_upper_bound(X3,identity),X2) = least_upper_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c270,c273]) ).
cnf(c275,plain,
multiply(least_upper_bound(greatest_lower_bound(X3,inverse(X2)),identity),X2) = least_upper_bound(X2,multiply(greatest_lower_bound(X3,inverse(X2)),X2)),
inference(substitution,[status(thm)],[c274]) ).
cnf(c276,plain,
greatest_lower_bound(inverse(X2),X3) = greatest_lower_bound(X3,inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c277,plain,
greatest_lower_bound(X3,inverse(X2)) = greatest_lower_bound(inverse(X2),X3),
inference(symmetry,[status(thm)],[c276]) ).
cnf(c278,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),X2) = multiply(greatest_lower_bound(inverse(X2),X3),X2),
inference(congruence,[status(thm)],[c277]) ).
cnf(c279,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c280,plain,
greatest_lower_bound(multiply(inverse(X2),X2),multiply(X3,X2)) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c281,plain,
multiply(greatest_lower_bound(inverse(X2),X3),X2) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c279,c280]) ).
cnf(c282,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),X2) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c278,c281]) ).
cnf(c283,plain,
least_upper_bound(X2,multiply(greatest_lower_bound(X3,inverse(X2)),X2)) = least_upper_bound(X2,greatest_lower_bound(identity,multiply(X3,X2))),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
multiply(least_upper_bound(greatest_lower_bound(X3,inverse(X2)),identity),X2) = least_upper_bound(X2,greatest_lower_bound(identity,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c275,c283]) ).
cnf(c285,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(X3,inverse(X2))),X2) = least_upper_bound(X2,greatest_lower_bound(identity,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c267,c284]) ).
cnf(c286,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),b) = least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b))),
inference(substitution,[status(thm)],[c285]) ).
cnf(c287,plain,
least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b))) = multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),b),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b))) = greatest_lower_bound(inverse(a),greatest_lower_bound(identity,inverse(b))),
inference(substitution,[status(thm)],[c45]) ).
cnf(c289,plain,
greatest_lower_bound(inverse(b),greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))),
inference(substitution,[status(thm)],[c140]) ).
cnf(c290,plain,
greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))) = greatest_lower_bound(inverse(b),greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))),
inference(symmetry,[status(thm)],[c289]) ).
cnf(c291,plain,
greatest_lower_bound(inverse(b),greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(inverse(b),identity),
inference(congruence,[status(thm)],[c59]) ).
cnf(c292,plain,
greatest_lower_bound(inverse(b),identity) = greatest_lower_bound(identity,inverse(b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c293,plain,
greatest_lower_bound(inverse(b),greatest_lower_bound(least_upper_bound(a,inverse(a)),least_upper_bound(b,inverse(b)))) = greatest_lower_bound(identity,inverse(b)),
inference(transitivity,[status(thm)],[c291,c292]) ).
cnf(c294,plain,
greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))) = greatest_lower_bound(identity,inverse(b)),
inference(transitivity,[status(thm)],[c290,c293]) ).
cnf(c295,plain,
greatest_lower_bound(identity,inverse(b)) = greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a))),
inference(symmetry,[status(thm)],[c294]) ).
cnf(c296,plain,
greatest_lower_bound(inverse(a),greatest_lower_bound(identity,inverse(b))) = greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a)))),
inference(congruence,[status(thm)],[c295]) ).
cnf(c297,plain,
greatest_lower_bound(inverse(a),greatest_lower_bound(inverse(b),least_upper_bound(a,inverse(a)))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c140]) ).
cnf(c298,plain,
greatest_lower_bound(inverse(a),greatest_lower_bound(identity,inverse(b))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(transitivity,[status(thm)],[c296,c297]) ).
cnf(c299,plain,
greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(transitivity,[status(thm)],[c288,c298]) ).
cnf(c300,plain,
greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))) = least_upper_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b)))),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c303,plain,
least_upper_bound(identity,greatest_lower_bound(identity,greatest_lower_bound(inverse(a),inverse(b)))) = identity,
inference(substitution,[status(thm)],[c302]) ).
cnf(c304,plain,
least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))) = identity,
inference(transitivity,[status(thm)],[c301,c303]) ).
cnf(c305,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),b) = multiply(identity,b),
inference(congruence,[status(thm)],[c304]) ).
cnf(c306,plain,
multiply(identity,b) = b,
inference(substitution,[status(thm)],[c16]) ).
cnf(c307,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),b) = b,
inference(transitivity,[status(thm)],[c305,c306]) ).
cnf(c308,plain,
least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b))) = b,
inference(transitivity,[status(thm)],[c287,c307]) ).
cnf(c309,plain,
multiply(a,least_upper_bound(b,greatest_lower_bound(identity,multiply(inverse(a),b)))) = multiply(a,b),
inference(congruence,[status(thm)],[c308]) ).
cnf(c310,plain,
least_upper_bound(multiply(a,b),multiply(a,greatest_lower_bound(identity,multiply(inverse(a),b)))) = multiply(a,b),
inference(transitivity,[status(thm)],[c264,c309]) ).
cnf(c311,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(b,multiply(a,identity))) = multiply(a,b),
inference(transitivity,[status(thm)],[c261,c310]) ).
cnf(c312,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(b,a)) = multiply(a,b),
inference(transitivity,[status(thm)],[c243,c311]) ).
cnf(c313,plain,
least_upper_bound(multiply(a,b),greatest_lower_bound(a,b)) = multiply(a,b),
inference(transitivity,[status(thm)],[c239,c312]) ).
cnf(c314,plain,
multiply(a,b) = least_upper_bound(multiply(a,b),greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c315,plain,
greatest_lower_bound(greatest_lower_bound(a,b),multiply(a,b)) = greatest_lower_bound(greatest_lower_bound(a,b),least_upper_bound(multiply(a,b),greatest_lower_bound(a,b))),
inference(congruence,[status(thm)],[c314]) ).
cnf(c316,plain,
greatest_lower_bound(greatest_lower_bound(a,b),least_upper_bound(multiply(a,b),greatest_lower_bound(a,b))) = greatest_lower_bound(a,b),
inference(substitution,[status(thm)],[c136]) ).
cnf(c317,plain,
greatest_lower_bound(greatest_lower_bound(a,b),multiply(a,b)) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[c315,c316]) ).
cnf(c318,plain,
greatest_lower_bound(a,greatest_lower_bound(b,multiply(a,b))) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[c236,c317]) ).
cnf(c319,plain,
greatest_lower_bound(a,greatest_lower_bound(multiply(a,b),b)) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[c235,c318]) ).
cnf(c320,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(a,b)) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[c232,c319]) ).
cnf(c321,plain,
greatest_lower_bound(multiply(a,b),identity) = greatest_lower_bound(a,b),
inference(transitivity,[status(thm)],[c231,c320]) ).
cnf(c322,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(a,b)),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(identity,greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c324,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(a,b)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,b))),
inference(congruence,[status(thm)],[c323]) ).
cnf(c325,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,X2)) = greatest_lower_bound(greatest_lower_bound(identity,a),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c326,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(greatest_lower_bound(identity,a),X2)),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
greatest_lower_bound(X2,greatest_lower_bound(identity,a)) = greatest_lower_bound(greatest_lower_bound(identity,a),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c328,plain,
greatest_lower_bound(greatest_lower_bound(identity,a),X2) = greatest_lower_bound(X2,greatest_lower_bound(identity,a)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(X2,greatest_lower_bound(identity,a))),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
greatest_lower_bound(X2,greatest_lower_bound(identity,a)) = greatest_lower_bound(identity,greatest_lower_bound(X2,a)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c331,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(X2,greatest_lower_bound(identity,a))) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(X2,a))),
inference(congruence,[status(thm)],[c330]) ).
cnf(c332,plain,
greatest_lower_bound(a,X2) = greatest_lower_bound(X2,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c333,plain,
greatest_lower_bound(X2,a) = greatest_lower_bound(a,X2),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
greatest_lower_bound(identity,greatest_lower_bound(X2,a)) = greatest_lower_bound(identity,greatest_lower_bound(a,X2)),
inference(congruence,[status(thm)],[c333]) ).
cnf(c335,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(X2,a))) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,X2))),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,X2)) = greatest_lower_bound(greatest_lower_bound(identity,a),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c337,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(greatest_lower_bound(identity,a),X2)),
inference(congruence,[status(thm)],[c336]) ).
cnf(c338,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,a)),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c339,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),a)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c340,plain,
multiply(least_upper_bound(a,inverse(a)),a) = least_upper_bound(identity,multiply(a,a)),
inference(substitution,[status(thm)],[c189]) ).
cnf(c341,plain,
least_upper_bound(identity,multiply(a,a)) = multiply(least_upper_bound(a,inverse(a)),a),
inference(symmetry,[status(thm)],[c340]) ).
cnf(c342,plain,
greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(a,a))) = greatest_lower_bound(multiply(b,a),multiply(least_upper_bound(a,inverse(a)),a)),
inference(congruence,[status(thm)],[c341]) ).
cnf(c343,plain,
multiply(greatest_lower_bound(b,least_upper_bound(a,inverse(a))),a) = greatest_lower_bound(multiply(b,a),multiply(least_upper_bound(a,inverse(a)),a)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c344,plain,
greatest_lower_bound(multiply(b,a),multiply(least_upper_bound(a,inverse(a)),a)) = multiply(greatest_lower_bound(b,least_upper_bound(a,inverse(a))),a),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
multiply(greatest_lower_bound(b,least_upper_bound(a,inverse(a))),a) = multiply(greatest_lower_bound(identity,b),a),
inference(congruence,[status(thm)],[c63]) ).
cnf(c346,plain,
greatest_lower_bound(multiply(b,a),multiply(identity,a)) = multiply(greatest_lower_bound(identity,b),a),
inference(substitution,[status(thm)],[c211]) ).
cnf(c347,plain,
multiply(greatest_lower_bound(identity,b),a) = greatest_lower_bound(multiply(b,a),multiply(identity,a)),
inference(symmetry,[status(thm)],[c346]) ).
cnf(c348,plain,
multiply(identity,a) = a,
inference(substitution,[status(thm)],[c16]) ).
cnf(c349,plain,
greatest_lower_bound(multiply(b,a),multiply(identity,a)) = greatest_lower_bound(multiply(b,a),a),
inference(congruence,[status(thm)],[c348]) ).
cnf(c350,plain,
multiply(greatest_lower_bound(identity,b),a) = greatest_lower_bound(multiply(b,a),a),
inference(transitivity,[status(thm)],[c347,c349]) ).
cnf(c351,plain,
multiply(greatest_lower_bound(b,least_upper_bound(a,inverse(a))),a) = greatest_lower_bound(multiply(b,a),a),
inference(transitivity,[status(thm)],[c345,c350]) ).
cnf(c352,plain,
greatest_lower_bound(multiply(b,a),multiply(least_upper_bound(a,inverse(a)),a)) = greatest_lower_bound(multiply(b,a),a),
inference(transitivity,[status(thm)],[c344,c351]) ).
cnf(c353,plain,
greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(a,a))) = greatest_lower_bound(multiply(b,a),a),
inference(transitivity,[status(thm)],[c342,c352]) ).
cnf(c354,plain,
greatest_lower_bound(multiply(b,a),a) = greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(a,a))),
inference(symmetry,[status(thm)],[c353]) ).
cnf(c355,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),a)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(a,a)))),
inference(congruence,[status(thm)],[c354]) ).
cnf(c356,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(a,a)))) = greatest_lower_bound(identity,multiply(b,a)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c357,plain,
greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(multiply(b,a),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c358,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(a,a)))) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c356,c357]) ).
cnf(c359,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),a)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c355,c358]) ).
cnf(c360,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,a)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c339,c359]) ).
cnf(c361,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,a)),X2) = greatest_lower_bound(greatest_lower_bound(multiply(b,a),identity),X2),
inference(congruence,[status(thm)],[c360]) ).
cnf(c362,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,X2)) = greatest_lower_bound(greatest_lower_bound(multiply(b,a),identity),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c363,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,a),identity),X2) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,X2)),
inference(symmetry,[status(thm)],[c362]) ).
cnf(c364,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c365,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,X2)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c364]) ).
cnf(c366,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(X2,identity)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c367,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(X2,identity)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(symmetry,[status(thm)],[c366]) ).
cnf(c368,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c365,c367]) ).
cnf(c369,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,a),identity),X2) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c363,c368]) ).
cnf(c370,plain,
greatest_lower_bound(greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,a)),X2) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c361,c369]) ).
cnf(c371,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c338,c370]) ).
cnf(c372,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c337,c371]) ).
cnf(c373,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(X2,a))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c335,c372]) ).
cnf(c374,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(X2,greatest_lower_bound(identity,a))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c331,c373]) ).
cnf(c375,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(greatest_lower_bound(identity,a),X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c329,c374]) ).
cnf(c376,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,X2))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,a),identity)),
inference(transitivity,[status(thm)],[c326,c375]) ).
cnf(c377,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,b))) = greatest_lower_bound(b,greatest_lower_bound(multiply(b,a),identity)),
inference(substitution,[status(thm)],[c376]) ).
cnf(c378,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(b,identity)) = greatest_lower_bound(b,greatest_lower_bound(multiply(b,a),identity)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c379,plain,
greatest_lower_bound(b,greatest_lower_bound(multiply(b,a),identity)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(b,identity)),
inference(symmetry,[status(thm)],[c378]) ).
cnf(c380,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c381,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(b,identity)) = greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,b)),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),b)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c383,plain,
least_upper_bound(inverse(X3),X2) = least_upper_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c384,plain,
least_upper_bound(X2,inverse(X3)) = least_upper_bound(inverse(X3),X2),
inference(symmetry,[status(thm)],[c383]) ).
cnf(c385,plain,
multiply(X3,least_upper_bound(X2,inverse(X3))) = multiply(X3,least_upper_bound(inverse(X3),X2)),
inference(congruence,[status(thm)],[c384]) ).
cnf(c386,plain,
multiply(inverse(inverse(X3)),least_upper_bound(inverse(X3),X2)) = multiply(X3,least_upper_bound(inverse(X3),X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c387,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = multiply(inverse(inverse(X3)),least_upper_bound(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c386]) ).
cnf(c388,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c262]) ).
cnf(c389,plain,
least_upper_bound(multiply(inverse(X3),X3),multiply(inverse(X3),X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c390,plain,
multiply(inverse(X3),least_upper_bound(X3,X2)) = least_upper_bound(identity,multiply(inverse(X3),X2)),
inference(transitivity,[status(thm)],[c388,c389]) ).
cnf(c391,plain,
multiply(inverse(inverse(X3)),least_upper_bound(inverse(X3),X2)) = least_upper_bound(identity,multiply(inverse(inverse(X3)),X2)),
inference(substitution,[status(thm)],[c390]) ).
cnf(c392,plain,
least_upper_bound(identity,multiply(inverse(inverse(X3)),X2)) = least_upper_bound(identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c88]) ).
cnf(c393,plain,
multiply(inverse(inverse(X3)),least_upper_bound(inverse(X3),X2)) = least_upper_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c391,c392]) ).
cnf(c394,plain,
multiply(X3,least_upper_bound(inverse(X3),X2)) = least_upper_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c387,c393]) ).
cnf(c395,plain,
multiply(X3,least_upper_bound(X2,inverse(X3))) = least_upper_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c385,c394]) ).
cnf(c396,plain,
multiply(b,least_upper_bound(b,inverse(b))) = least_upper_bound(identity,multiply(b,b)),
inference(substitution,[status(thm)],[c395]) ).
cnf(c397,plain,
least_upper_bound(identity,multiply(b,b)) = multiply(b,least_upper_bound(b,inverse(b))),
inference(symmetry,[status(thm)],[c396]) ).
cnf(c398,plain,
greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(b,b))) = greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(b,inverse(b)))),
inference(congruence,[status(thm)],[c397]) ).
cnf(c399,plain,
multiply(b,greatest_lower_bound(a,least_upper_bound(b,inverse(b)))) = greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(b,inverse(b)))),
inference(substitution,[status(thm)],[c105]) ).
cnf(c400,plain,
greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(b,inverse(b)))) = multiply(b,greatest_lower_bound(a,least_upper_bound(b,inverse(b)))),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
multiply(b,greatest_lower_bound(a,least_upper_bound(b,inverse(b)))) = multiply(b,greatest_lower_bound(identity,a)),
inference(congruence,[status(thm)],[c205]) ).
cnf(c402,plain,
multiply(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c403,plain,
greatest_lower_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c402]) ).
cnf(c404,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c405,plain,
multiply(X4,greatest_lower_bound(X2,X3)) = multiply(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c404]) ).
cnf(c406,plain,
greatest_lower_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c403,c405]) ).
cnf(c407,plain,
greatest_lower_bound(multiply(b,a),multiply(b,identity)) = multiply(b,greatest_lower_bound(identity,a)),
inference(substitution,[status(thm)],[c406]) ).
cnf(c408,plain,
multiply(b,greatest_lower_bound(identity,a)) = greatest_lower_bound(multiply(b,a),multiply(b,identity)),
inference(symmetry,[status(thm)],[c407]) ).
cnf(c409,plain,
multiply(b,identity) = b,
inference(substitution,[status(thm)],[c95]) ).
cnf(c410,plain,
greatest_lower_bound(multiply(b,a),multiply(b,identity)) = greatest_lower_bound(multiply(b,a),b),
inference(congruence,[status(thm)],[c409]) ).
cnf(c411,plain,
multiply(b,greatest_lower_bound(identity,a)) = greatest_lower_bound(multiply(b,a),b),
inference(transitivity,[status(thm)],[c408,c410]) ).
cnf(c412,plain,
multiply(b,greatest_lower_bound(a,least_upper_bound(b,inverse(b)))) = greatest_lower_bound(multiply(b,a),b),
inference(transitivity,[status(thm)],[c401,c411]) ).
cnf(c413,plain,
greatest_lower_bound(multiply(b,a),multiply(b,least_upper_bound(b,inverse(b)))) = greatest_lower_bound(multiply(b,a),b),
inference(transitivity,[status(thm)],[c400,c412]) ).
cnf(c414,plain,
greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(b,b))) = greatest_lower_bound(multiply(b,a),b),
inference(transitivity,[status(thm)],[c398,c413]) ).
cnf(c415,plain,
greatest_lower_bound(multiply(b,a),b) = greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(b,b))),
inference(symmetry,[status(thm)],[c414]) ).
cnf(c416,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),b)) = greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(b,b)))),
inference(congruence,[status(thm)],[c415]) ).
cnf(c417,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(b,b)))) = greatest_lower_bound(identity,multiply(b,a)),
inference(substitution,[status(thm)],[c56]) ).
cnf(c418,plain,
greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(multiply(b,a),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c419,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),least_upper_bound(identity,multiply(b,b)))) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c417,c418]) ).
cnf(c420,plain,
greatest_lower_bound(identity,greatest_lower_bound(multiply(b,a),b)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c416,c419]) ).
cnf(c421,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,b)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c382,c420]) ).
cnf(c422,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(b,identity)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c381,c421]) ).
cnf(c423,plain,
greatest_lower_bound(b,greatest_lower_bound(multiply(b,a),identity)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c379,c422]) ).
cnf(c424,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(identity,greatest_lower_bound(a,b))) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c377,c423]) ).
cnf(c425,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(a,b)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c324,c424]) ).
cnf(c426,plain,
greatest_lower_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c322,c425]) ).
cnf(c427,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(multiply(b,a),identity)) = greatest_lower_bound(multiply(b,a),identity),
inference(transitivity,[status(thm)],[c46,c426]) ).
cnf(c428,plain,
greatest_lower_bound(multiply(b,a),identity) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(multiply(b,a),identity)),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
greatest_lower_bound(identity,multiply(b,a)) = greatest_lower_bound(multiply(b,a),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c430,plain,
greatest_lower_bound(multiply(b,a),identity) = greatest_lower_bound(identity,multiply(b,a)),
inference(symmetry,[status(thm)],[c429]) ).
cnf(c431,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(multiply(b,a),identity)) = greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,multiply(b,a))),
inference(congruence,[status(thm)],[c430]) ).
cnf(c432,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,multiply(b,a))) = greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),multiply(b,a)),
inference(substitution,[status(thm)],[c39]) ).
cnf(c433,plain,
least_upper_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity)) = least_upper_bound(multiply(b,a),greatest_lower_bound(a,b)),
inference(congruence,[status(thm)],[c321]) ).
cnf(c434,plain,
multiply(b,identity) = b,
inference(substitution,[status(thm)],[c95]) ).
cnf(c435,plain,
b = multiply(b,identity),
inference(symmetry,[status(thm)],[c434]) ).
cnf(c436,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(a,multiply(b,identity)),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
least_upper_bound(multiply(b,a),greatest_lower_bound(a,b)) = least_upper_bound(multiply(b,a),greatest_lower_bound(a,multiply(b,identity))),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
multiply(b,greatest_lower_bound(identity,multiply(inverse(b),a))) = greatest_lower_bound(a,multiply(b,identity)),
inference(substitution,[status(thm)],[c258]) ).
cnf(c439,plain,
greatest_lower_bound(a,multiply(b,identity)) = multiply(b,greatest_lower_bound(identity,multiply(inverse(b),a))),
inference(symmetry,[status(thm)],[c438]) ).
cnf(c440,plain,
least_upper_bound(multiply(b,a),greatest_lower_bound(a,multiply(b,identity))) = least_upper_bound(multiply(b,a),multiply(b,greatest_lower_bound(identity,multiply(inverse(b),a)))),
inference(congruence,[status(thm)],[c439]) ).
cnf(c441,plain,
multiply(b,least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a)))) = least_upper_bound(multiply(b,a),multiply(b,greatest_lower_bound(identity,multiply(inverse(b),a)))),
inference(substitution,[status(thm)],[c262]) ).
cnf(c442,plain,
least_upper_bound(multiply(b,a),multiply(b,greatest_lower_bound(identity,multiply(inverse(b),a)))) = multiply(b,least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a)))),
inference(symmetry,[status(thm)],[c441]) ).
cnf(c443,plain,
least_upper_bound(greatest_lower_bound(inverse(X3),X2),identity) = least_upper_bound(identity,greatest_lower_bound(inverse(X3),X2)),
inference(substitution,[status(thm)],[c131]) ).
cnf(c444,plain,
least_upper_bound(identity,greatest_lower_bound(inverse(X3),X2)) = least_upper_bound(greatest_lower_bound(inverse(X3),X2),identity),
inference(symmetry,[status(thm)],[c443]) ).
cnf(c445,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(X3),X2)),X3) = multiply(least_upper_bound(greatest_lower_bound(inverse(X3),X2),identity),X3),
inference(congruence,[status(thm)],[c444]) ).
cnf(c446,plain,
multiply(least_upper_bound(greatest_lower_bound(inverse(X3),X2),identity),X3) = least_upper_bound(X3,multiply(greatest_lower_bound(inverse(X3),X2),X3)),
inference(substitution,[status(thm)],[c274]) ).
cnf(c447,plain,
greatest_lower_bound(X2,inverse(X3)) = greatest_lower_bound(inverse(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c448,plain,
greatest_lower_bound(inverse(X3),X2) = greatest_lower_bound(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c447]) ).
cnf(c449,plain,
multiply(greatest_lower_bound(inverse(X3),X2),X3) = multiply(greatest_lower_bound(X2,inverse(X3)),X3),
inference(congruence,[status(thm)],[c448]) ).
cnf(c450,plain,
multiply(greatest_lower_bound(X2,inverse(X3)),X3) = greatest_lower_bound(identity,multiply(X2,X3)),
inference(substitution,[status(thm)],[c282]) ).
cnf(c451,plain,
multiply(greatest_lower_bound(inverse(X3),X2),X3) = greatest_lower_bound(identity,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c449,c450]) ).
cnf(c452,plain,
least_upper_bound(X3,multiply(greatest_lower_bound(inverse(X3),X2),X3)) = least_upper_bound(X3,greatest_lower_bound(identity,multiply(X2,X3))),
inference(congruence,[status(thm)],[c451]) ).
cnf(c453,plain,
multiply(least_upper_bound(greatest_lower_bound(inverse(X3),X2),identity),X3) = least_upper_bound(X3,greatest_lower_bound(identity,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c446,c452]) ).
cnf(c454,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(X3),X2)),X3) = least_upper_bound(X3,greatest_lower_bound(identity,multiply(X2,X3))),
inference(transitivity,[status(thm)],[c445,c453]) ).
cnf(c455,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),a) = least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))),
inference(substitution,[status(thm)],[c454]) ).
cnf(c456,plain,
least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))) = multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),a),
inference(symmetry,[status(thm)],[c455]) ).
cnf(c457,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),a) = multiply(identity,a),
inference(congruence,[status(thm)],[c304]) ).
cnf(c458,plain,
multiply(identity,a) = a,
inference(substitution,[status(thm)],[c16]) ).
cnf(c459,plain,
multiply(least_upper_bound(identity,greatest_lower_bound(inverse(a),inverse(b))),a) = a,
inference(transitivity,[status(thm)],[c457,c458]) ).
cnf(c460,plain,
least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a))) = a,
inference(transitivity,[status(thm)],[c456,c459]) ).
cnf(c461,plain,
multiply(b,least_upper_bound(a,greatest_lower_bound(identity,multiply(inverse(b),a)))) = multiply(b,a),
inference(congruence,[status(thm)],[c460]) ).
cnf(c462,plain,
least_upper_bound(multiply(b,a),multiply(b,greatest_lower_bound(identity,multiply(inverse(b),a)))) = multiply(b,a),
inference(transitivity,[status(thm)],[c442,c461]) ).
cnf(c463,plain,
least_upper_bound(multiply(b,a),greatest_lower_bound(a,multiply(b,identity))) = multiply(b,a),
inference(transitivity,[status(thm)],[c440,c462]) ).
cnf(c464,plain,
least_upper_bound(multiply(b,a),greatest_lower_bound(a,b)) = multiply(b,a),
inference(transitivity,[status(thm)],[c437,c463]) ).
cnf(c465,plain,
least_upper_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity)) = multiply(b,a),
inference(transitivity,[status(thm)],[c433,c464]) ).
cnf(c466,plain,
multiply(b,a) = least_upper_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity)),
inference(symmetry,[status(thm)],[c465]) ).
cnf(c467,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),multiply(b,a)) = greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),least_upper_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity))),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),least_upper_bound(multiply(b,a),greatest_lower_bound(multiply(a,b),identity))) = greatest_lower_bound(multiply(a,b),identity),
inference(substitution,[status(thm)],[c136]) ).
cnf(c469,plain,
greatest_lower_bound(greatest_lower_bound(multiply(a,b),identity),multiply(b,a)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c467,c468]) ).
cnf(c470,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(identity,multiply(b,a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c432,c469]) ).
cnf(c471,plain,
greatest_lower_bound(multiply(a,b),greatest_lower_bound(multiply(b,a),identity)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c431,c470]) ).
cnf(c472,plain,
greatest_lower_bound(multiply(b,a),identity) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c428,c471]) ).
cnf(c473,plain,
greatest_lower_bound(multiply(a,b),identity) = greatest_lower_bound(multiply(b,a),identity),
inference(symmetry,[status(thm)],[c472]) ).
cnf(c474,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),X2) = multiply(greatest_lower_bound(multiply(b,a),identity),X2),
inference(congruence,[status(thm)],[c473]) ).
cnf(c475,plain,
multiply(b,inverse(b)) = identity,
inference(substitution,[status(thm)],[c152]) ).
cnf(c476,plain,
identity = multiply(b,inverse(b)),
inference(symmetry,[status(thm)],[c475]) ).
cnf(c477,plain,
greatest_lower_bound(multiply(b,a),identity) = greatest_lower_bound(multiply(b,a),multiply(b,inverse(b))),
inference(congruence,[status(thm)],[c476]) ).
cnf(c478,plain,
multiply(greatest_lower_bound(multiply(b,a),identity),X2) = multiply(greatest_lower_bound(multiply(b,a),multiply(b,inverse(b))),X2),
inference(congruence,[status(thm)],[c477]) ).
cnf(c479,plain,
greatest_lower_bound(multiply(X4,X3),multiply(X4,X2)) = multiply(X4,greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c406]) ).
cnf(c480,plain,
multiply(greatest_lower_bound(multiply(X5,X4),multiply(X5,X3)),X2) = multiply(multiply(X5,greatest_lower_bound(X3,X4)),X2),
inference(congruence,[status(thm)],[c479]) ).
cnf(c481,plain,
multiply(multiply(X5,greatest_lower_bound(X3,X4)),X2) = multiply(X5,multiply(greatest_lower_bound(X3,X4),X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c482,plain,
multiply(greatest_lower_bound(multiply(X5,X4),multiply(X5,X3)),X2) = multiply(X5,multiply(greatest_lower_bound(X3,X4),X2)),
inference(transitivity,[status(thm)],[c480,c481]) ).
cnf(c483,plain,
multiply(greatest_lower_bound(multiply(b,a),multiply(b,inverse(b))),X2) = multiply(b,multiply(greatest_lower_bound(inverse(b),a),X2)),
inference(substitution,[status(thm)],[c482]) ).
cnf(c484,plain,
greatest_lower_bound(inverse(b),a) = greatest_lower_bound(a,inverse(b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c485,plain,
multiply(greatest_lower_bound(inverse(b),a),X2) = multiply(greatest_lower_bound(a,inverse(b)),X2),
inference(congruence,[status(thm)],[c484]) ).
cnf(c486,plain,
multiply(b,multiply(greatest_lower_bound(inverse(b),a),X2)) = multiply(b,multiply(greatest_lower_bound(a,inverse(b)),X2)),
inference(congruence,[status(thm)],[c485]) ).
cnf(c487,plain,
multiply(greatest_lower_bound(multiply(b,a),multiply(b,inverse(b))),X2) = multiply(b,multiply(greatest_lower_bound(a,inverse(b)),X2)),
inference(transitivity,[status(thm)],[c483,c486]) ).
cnf(c488,plain,
multiply(greatest_lower_bound(multiply(b,a),identity),X2) = multiply(b,multiply(greatest_lower_bound(a,inverse(b)),X2)),
inference(transitivity,[status(thm)],[c478,c487]) ).
cnf(c489,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),X2) = multiply(b,multiply(greatest_lower_bound(a,inverse(b)),X2)),
inference(transitivity,[status(thm)],[c474,c488]) ).
cnf(c490,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))) = multiply(b,multiply(greatest_lower_bound(a,inverse(b)),inverse(multiply(b,a)))),
inference(substitution,[status(thm)],[c489]) ).
cnf(c491,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c492,plain,
multiply(X4,multiply(X3,X2)) = multiply(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c491]) ).
cnf(c493,plain,
greatest_lower_bound(multiply(X5,multiply(X4,X3)),multiply(X2,X3)) = greatest_lower_bound(multiply(multiply(X5,X4),X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c492]) ).
cnf(c494,plain,
multiply(greatest_lower_bound(multiply(X5,X4),X2),X3) = greatest_lower_bound(multiply(multiply(X5,X4),X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c495,plain,
greatest_lower_bound(multiply(multiply(X5,X4),X3),multiply(X2,X3)) = multiply(greatest_lower_bound(multiply(X5,X4),X2),X3),
inference(symmetry,[status(thm)],[c494]) ).
cnf(c496,plain,
greatest_lower_bound(multiply(X4,X3),X2) = greatest_lower_bound(X2,multiply(X4,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c497,plain,
multiply(greatest_lower_bound(multiply(X5,X4),X2),X3) = multiply(greatest_lower_bound(X2,multiply(X5,X4)),X3),
inference(congruence,[status(thm)],[c496]) ).
cnf(c498,plain,
greatest_lower_bound(multiply(multiply(X5,X4),X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,multiply(X5,X4)),X3),
inference(transitivity,[status(thm)],[c495,c497]) ).
cnf(c499,plain,
greatest_lower_bound(multiply(X5,multiply(X4,X3)),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,multiply(X5,X4)),X3),
inference(transitivity,[status(thm)],[c493,c498]) ).
cnf(c500,plain,
greatest_lower_bound(multiply(X4,multiply(X3,X2)),multiply(X4,X2)) = multiply(greatest_lower_bound(X4,multiply(X4,X3)),X2),
inference(substitution,[status(thm)],[c499]) ).
cnf(c501,plain,
multiply(greatest_lower_bound(X4,multiply(X4,X3)),X2) = greatest_lower_bound(multiply(X4,multiply(X3,X2)),multiply(X4,X2)),
inference(symmetry,[status(thm)],[c500]) ).
cnf(c502,plain,
multiply(X4,greatest_lower_bound(multiply(X3,X2),X2)) = greatest_lower_bound(multiply(X4,multiply(X3,X2)),multiply(X4,X2)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c503,plain,
greatest_lower_bound(multiply(X4,multiply(X3,X2)),multiply(X4,X2)) = multiply(X4,greatest_lower_bound(multiply(X3,X2),X2)),
inference(symmetry,[status(thm)],[c502]) ).
cnf(c504,plain,
greatest_lower_bound(multiply(X3,X2),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c505,plain,
multiply(X4,greatest_lower_bound(multiply(X3,X2),X2)) = multiply(X4,greatest_lower_bound(X2,multiply(X3,X2))),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
greatest_lower_bound(multiply(X4,multiply(X3,X2)),multiply(X4,X2)) = multiply(X4,greatest_lower_bound(X2,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c503,c505]) ).
cnf(c507,plain,
multiply(greatest_lower_bound(X4,multiply(X4,X3)),X2) = multiply(X4,greatest_lower_bound(X2,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c501,c506]) ).
cnf(c508,plain,
multiply(greatest_lower_bound(inverse(X4),multiply(inverse(X4),multiply(X4,X2))),X3) = multiply(inverse(X4),greatest_lower_bound(X3,multiply(multiply(X4,X2),X3))),
inference(substitution,[status(thm)],[c507]) ).
cnf(c509,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(multiply(X4,X2),X3))) = multiply(greatest_lower_bound(inverse(X4),multiply(inverse(X4),multiply(X4,X2))),X3),
inference(symmetry,[status(thm)],[c508]) ).
cnf(c510,plain,
greatest_lower_bound(inverse(X3),multiply(inverse(X3),multiply(X3,X2))) = greatest_lower_bound(inverse(X3),X2),
inference(congruence,[status(thm)],[c27]) ).
cnf(c511,plain,
multiply(greatest_lower_bound(inverse(X4),multiply(inverse(X4),multiply(X4,X2))),X3) = multiply(greatest_lower_bound(inverse(X4),X2),X3),
inference(congruence,[status(thm)],[c510]) ).
cnf(c512,plain,
greatest_lower_bound(inverse(X3),X2) = greatest_lower_bound(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c513,plain,
multiply(greatest_lower_bound(inverse(X4),X2),X3) = multiply(greatest_lower_bound(X2,inverse(X4)),X3),
inference(congruence,[status(thm)],[c512]) ).
cnf(c514,plain,
multiply(greatest_lower_bound(inverse(X4),multiply(inverse(X4),multiply(X4,X2))),X3) = multiply(greatest_lower_bound(X2,inverse(X4)),X3),
inference(transitivity,[status(thm)],[c511,c513]) ).
cnf(c515,plain,
multiply(inverse(X4),greatest_lower_bound(X3,multiply(multiply(X4,X2),X3))) = multiply(greatest_lower_bound(X2,inverse(X4)),X3),
inference(transitivity,[status(thm)],[c509,c514]) ).
cnf(c516,plain,
multiply(inverse(X2),greatest_lower_bound(inverse(multiply(X2,X3)),multiply(multiply(X2,X3),inverse(multiply(X2,X3))))) = multiply(greatest_lower_bound(X3,inverse(X2)),inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c515]) ).
cnf(c517,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),inverse(multiply(X2,X3))) = multiply(inverse(X2),greatest_lower_bound(inverse(multiply(X2,X3)),multiply(multiply(X2,X3),inverse(multiply(X2,X3))))),
inference(symmetry,[status(thm)],[c516]) ).
cnf(c518,plain,
multiply(multiply(X2,X3),inverse(multiply(X2,X3))) = identity,
inference(substitution,[status(thm)],[c152]) ).
cnf(c519,plain,
greatest_lower_bound(inverse(multiply(X2,X3)),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))) = greatest_lower_bound(inverse(multiply(X2,X3)),identity),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
multiply(inverse(X2),greatest_lower_bound(inverse(multiply(X2,X3)),multiply(multiply(X2,X3),inverse(multiply(X2,X3))))) = multiply(inverse(X2),greatest_lower_bound(inverse(multiply(X2,X3)),identity)),
inference(congruence,[status(thm)],[c519]) ).
cnf(c521,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c522,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c521]) ).
cnf(c523,plain,
multiply(X3,greatest_lower_bound(X2,identity)) = multiply(X3,greatest_lower_bound(identity,X2)),
inference(congruence,[status(thm)],[c522]) ).
cnf(c524,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c525,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c95]) ).
cnf(c526,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c524,c525]) ).
cnf(c527,plain,
multiply(X3,greatest_lower_bound(X2,identity)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c523,c526]) ).
cnf(c528,plain,
multiply(inverse(X2),greatest_lower_bound(inverse(multiply(X2,X3)),identity)) = greatest_lower_bound(inverse(X2),multiply(inverse(X2),inverse(multiply(X2,X3)))),
inference(substitution,[status(thm)],[c527]) ).
cnf(c529,plain,
multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c530,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))),
inference(symmetry,[status(thm)],[c529]) ).
cnf(c531,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c532,plain,
multiply(inverse(X4),multiply(multiply(X4,X3),X2)) = multiply(inverse(X4),multiply(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c531]) ).
cnf(c533,plain,
multiply(inverse(X4),multiply(X4,multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c534,plain,
multiply(inverse(X4),multiply(multiply(X4,X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c532,c533]) ).
cnf(c535,plain,
multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))) = multiply(X3,inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c534]) ).
cnf(c536,plain,
multiply(X3,inverse(multiply(X2,X3))) = multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))),
inference(symmetry,[status(thm)],[c535]) ).
cnf(c537,plain,
multiply(multiply(X2,X3),inverse(multiply(X2,X3))) = identity,
inference(substitution,[status(thm)],[c152]) ).
cnf(c538,plain,
multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))) = multiply(inverse(X2),identity),
inference(congruence,[status(thm)],[c537]) ).
cnf(c539,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(substitution,[status(thm)],[c95]) ).
cnf(c540,plain,
multiply(inverse(X2),multiply(multiply(X2,X3),inverse(multiply(X2,X3)))) = inverse(X2),
inference(transitivity,[status(thm)],[c538,c539]) ).
cnf(c541,plain,
multiply(X3,inverse(multiply(X2,X3))) = inverse(X2),
inference(transitivity,[status(thm)],[c536,c540]) ).
cnf(c542,plain,
multiply(X2,inverse(multiply(X3,X2))) = inverse(X3),
inference(substitution,[status(thm)],[c541]) ).
cnf(c543,plain,
multiply(inverse(X2),multiply(X2,inverse(multiply(X3,X2)))) = multiply(inverse(X2),inverse(X3)),
inference(congruence,[status(thm)],[c542]) ).
cnf(c544,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),inverse(X3)),
inference(transitivity,[status(thm)],[c530,c543]) ).
cnf(c545,plain,
inverse(multiply(X3,multiply(X2,X4))) = multiply(inverse(multiply(X2,X4)),inverse(X3)),
inference(substitution,[status(thm)],[c544]) ).
cnf(c546,plain,
multiply(inverse(multiply(X2,X4)),inverse(X3)) = inverse(multiply(X3,multiply(X2,X4))),
inference(symmetry,[status(thm)],[c545]) ).
cnf(c547,plain,
multiply(multiply(X3,X2),X4) = multiply(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c548,plain,
multiply(X3,multiply(X2,X4)) = multiply(multiply(X3,X2),X4),
inference(symmetry,[status(thm)],[c547]) ).
cnf(c549,plain,
inverse(multiply(X3,multiply(X2,X4))) = inverse(multiply(multiply(X3,X2),X4)),
inference(congruence,[status(thm)],[c548]) ).
cnf(c550,plain,
inverse(multiply(multiply(X3,X2),X4)) = multiply(inverse(X4),inverse(multiply(X3,X2))),
inference(substitution,[status(thm)],[c544]) ).
cnf(c551,plain,
inverse(multiply(X3,multiply(X2,X4))) = multiply(inverse(X4),inverse(multiply(X3,X2))),
inference(transitivity,[status(thm)],[c549,c550]) ).
cnf(c552,plain,
multiply(inverse(multiply(X2,X4)),inverse(X3)) = multiply(inverse(X4),inverse(multiply(X3,X2))),
inference(transitivity,[status(thm)],[c546,c551]) ).
cnf(c553,plain,
multiply(inverse(multiply(X3,X2)),inverse(X2)) = multiply(inverse(X2),inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c552]) ).
cnf(c554,plain,
multiply(inverse(X2),inverse(multiply(X2,X3))) = multiply(inverse(multiply(X3,X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c553]) ).
cnf(c555,plain,
greatest_lower_bound(inverse(X2),multiply(inverse(X2),inverse(multiply(X2,X3)))) = greatest_lower_bound(inverse(X2),multiply(inverse(multiply(X3,X2)),inverse(X2))),
inference(congruence,[status(thm)],[c554]) ).
cnf(c556,plain,
multiply(inverse(X2),greatest_lower_bound(inverse(multiply(X2,X3)),identity)) = greatest_lower_bound(inverse(X2),multiply(inverse(multiply(X3,X2)),inverse(X2))),
inference(transitivity,[status(thm)],[c528,c555]) ).
cnf(c557,plain,
multiply(inverse(X2),greatest_lower_bound(inverse(multiply(X2,X3)),multiply(multiply(X2,X3),inverse(multiply(X2,X3))))) = greatest_lower_bound(inverse(X2),multiply(inverse(multiply(X3,X2)),inverse(X2))),
inference(transitivity,[status(thm)],[c520,c556]) ).
cnf(c558,plain,
multiply(greatest_lower_bound(X3,inverse(X2)),inverse(multiply(X2,X3))) = greatest_lower_bound(inverse(X2),multiply(inverse(multiply(X3,X2)),inverse(X2))),
inference(transitivity,[status(thm)],[c517,c557]) ).
cnf(c559,plain,
multiply(greatest_lower_bound(a,inverse(b)),inverse(multiply(b,a))) = greatest_lower_bound(inverse(b),multiply(inverse(multiply(a,b)),inverse(b))),
inference(substitution,[status(thm)],[c558]) ).
cnf(c560,plain,
multiply(b,multiply(greatest_lower_bound(a,inverse(b)),inverse(multiply(b,a)))) = multiply(b,greatest_lower_bound(inverse(b),multiply(inverse(multiply(a,b)),inverse(b)))),
inference(congruence,[status(thm)],[c559]) ).
cnf(c561,plain,
greatest_lower_bound(X2,inverse(X3)) = greatest_lower_bound(inverse(X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c562,plain,
greatest_lower_bound(inverse(X3),X2) = greatest_lower_bound(X2,inverse(X3)),
inference(symmetry,[status(thm)],[c561]) ).
cnf(c563,plain,
multiply(X3,greatest_lower_bound(inverse(X3),X2)) = multiply(X3,greatest_lower_bound(X2,inverse(X3))),
inference(congruence,[status(thm)],[c562]) ).
cnf(c564,plain,
multiply(X3,greatest_lower_bound(inverse(X3),X2)) = greatest_lower_bound(identity,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c563,c113]) ).
cnf(c565,plain,
multiply(b,greatest_lower_bound(inverse(b),multiply(inverse(multiply(a,b)),inverse(b)))) = greatest_lower_bound(identity,multiply(b,multiply(inverse(multiply(a,b)),inverse(b)))),
inference(substitution,[status(thm)],[c564]) ).
cnf(c566,plain,
multiply(inverse(X3),multiply(multiply(X3,X4),multiply(inverse(multiply(X3,X4)),X2))) = multiply(X4,multiply(inverse(multiply(X3,X4)),X2)),
inference(substitution,[status(thm)],[c534]) ).
cnf(c567,plain,
multiply(X4,multiply(inverse(multiply(X3,X4)),X2)) = multiply(inverse(X3),multiply(multiply(X3,X4),multiply(inverse(multiply(X3,X4)),X2))),
inference(symmetry,[status(thm)],[c566]) ).
cnf(c568,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c88]) ).
cnf(c569,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c568]) ).
cnf(c570,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),X2)) = X2,
inference(substitution,[status(thm)],[c27]) ).
cnf(c571,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c569,c570]) ).
cnf(c572,plain,
multiply(multiply(X3,X4),multiply(inverse(multiply(X3,X4)),X2)) = X2,
inference(substitution,[status(thm)],[c571]) ).
cnf(c573,plain,
multiply(inverse(X3),multiply(multiply(X3,X4),multiply(inverse(multiply(X3,X4)),X2))) = multiply(inverse(X3),X2),
inference(congruence,[status(thm)],[c572]) ).
cnf(c574,plain,
multiply(X4,multiply(inverse(multiply(X3,X4)),X2)) = multiply(inverse(X3),X2),
inference(transitivity,[status(thm)],[c567,c573]) ).
cnf(c575,plain,
multiply(b,multiply(inverse(multiply(a,b)),inverse(b))) = multiply(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c574]) ).
cnf(c576,plain,
greatest_lower_bound(identity,multiply(b,multiply(inverse(multiply(a,b)),inverse(b)))) = greatest_lower_bound(identity,multiply(inverse(a),inverse(b))),
inference(congruence,[status(thm)],[c575]) ).
cnf(c577,plain,
inverse(multiply(b,a)) = multiply(inverse(a),inverse(b)),
inference(substitution,[status(thm)],[c544]) ).
cnf(c578,plain,
multiply(inverse(a),inverse(b)) = inverse(multiply(b,a)),
inference(symmetry,[status(thm)],[c577]) ).
cnf(c579,plain,
greatest_lower_bound(identity,multiply(inverse(a),inverse(b))) = greatest_lower_bound(identity,inverse(multiply(b,a))),
inference(congruence,[status(thm)],[c578]) ).
cnf(c580,plain,
greatest_lower_bound(identity,multiply(b,multiply(inverse(multiply(a,b)),inverse(b)))) = greatest_lower_bound(identity,inverse(multiply(b,a))),
inference(transitivity,[status(thm)],[c576,c579]) ).
cnf(c581,plain,
multiply(b,greatest_lower_bound(inverse(b),multiply(inverse(multiply(a,b)),inverse(b)))) = greatest_lower_bound(identity,inverse(multiply(b,a))),
inference(transitivity,[status(thm)],[c565,c580]) ).
cnf(c582,plain,
multiply(b,multiply(greatest_lower_bound(a,inverse(b)),inverse(multiply(b,a)))) = greatest_lower_bound(identity,inverse(multiply(b,a))),
inference(transitivity,[status(thm)],[c560,c581]) ).
cnf(c583,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))) = greatest_lower_bound(identity,inverse(multiply(b,a))),
inference(transitivity,[status(thm)],[c490,c582]) ).
cnf(c584,plain,
greatest_lower_bound(inverse(multiply(b,a)),multiply(multiply(a,b),inverse(multiply(b,a)))) = greatest_lower_bound(identity,inverse(multiply(b,a))),
inference(transitivity,[status(thm)],[c36,c583]) ).
cnf(c585,plain,
greatest_lower_bound(identity,inverse(multiply(b,a))) = greatest_lower_bound(inverse(multiply(b,a)),multiply(multiply(a,b),inverse(multiply(b,a)))),
inference(symmetry,[status(thm)],[c584]) ).
cnf(c586,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))) = greatest_lower_bound(inverse(multiply(b,a)),multiply(multiply(a,b),inverse(multiply(b,a)))),
inference(substitution,[status(thm)],[c19]) ).
cnf(c587,plain,
greatest_lower_bound(inverse(multiply(b,a)),multiply(multiply(a,b),inverse(multiply(b,a)))) = multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))),
inference(symmetry,[status(thm)],[c586]) ).
cnf(c588,plain,
multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(a,a))) = greatest_lower_bound(a,multiply(inverse(a),multiply(b,a))),
inference(substitution,[status(thm)],[c252]) ).
cnf(c589,plain,
greatest_lower_bound(a,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(a,a))),
inference(symmetry,[status(thm)],[c588]) ).
cnf(c590,plain,
greatest_lower_bound(multiply(b,X2),multiply(a,X2)) = multiply(greatest_lower_bound(a,b),X2),
inference(substitution,[status(thm)],[c211]) ).
cnf(c591,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(multiply(a,b),identity),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c592,plain,
multiply(greatest_lower_bound(a,b),X2) = multiply(greatest_lower_bound(multiply(a,b),identity),X2),
inference(congruence,[status(thm)],[c591]) ).
cnf(c593,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),X2) = greatest_lower_bound(X2,multiply(multiply(a,b),X2)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c594,plain,
multiply(greatest_lower_bound(a,b),X2) = greatest_lower_bound(X2,multiply(multiply(a,b),X2)),
inference(transitivity,[status(thm)],[c592,c593]) ).
cnf(c595,plain,
greatest_lower_bound(multiply(b,X2),multiply(a,X2)) = greatest_lower_bound(X2,multiply(multiply(a,b),X2)),
inference(transitivity,[status(thm)],[c590,c594]) ).
cnf(c596,plain,
greatest_lower_bound(multiply(b,a),multiply(a,a)) = greatest_lower_bound(a,multiply(multiply(a,b),a)),
inference(substitution,[status(thm)],[c595]) ).
cnf(c597,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),a) = greatest_lower_bound(a,multiply(multiply(a,b),a)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c598,plain,
greatest_lower_bound(a,multiply(multiply(a,b),a)) = multiply(greatest_lower_bound(multiply(a,b),identity),a),
inference(symmetry,[status(thm)],[c597]) ).
cnf(c599,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c95]) ).
cnf(c600,plain,
a = multiply(a,identity),
inference(symmetry,[status(thm)],[c599]) ).
cnf(c601,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),a) = multiply(greatest_lower_bound(multiply(a,b),identity),multiply(a,identity)),
inference(congruence,[status(thm)],[c600]) ).
cnf(c602,plain,
multiply(greatest_lower_bound(X2,identity),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c603,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(symmetry,[status(thm)],[c602]) ).
cnf(c604,plain,
multiply(greatest_lower_bound(X4,multiply(X3,X4)),X2) = multiply(multiply(greatest_lower_bound(X3,identity),X4),X2),
inference(congruence,[status(thm)],[c603]) ).
cnf(c605,plain,
multiply(multiply(greatest_lower_bound(X3,identity),X4),X2) = multiply(greatest_lower_bound(X3,identity),multiply(X4,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c606,plain,
multiply(greatest_lower_bound(X4,multiply(X3,X4)),X2) = multiply(greatest_lower_bound(X3,identity),multiply(X4,X2)),
inference(transitivity,[status(thm)],[c604,c605]) ).
cnf(c607,plain,
multiply(greatest_lower_bound(a,multiply(multiply(a,b),a)),X2) = multiply(greatest_lower_bound(multiply(a,b),identity),multiply(a,X2)),
inference(substitution,[status(thm)],[c606]) ).
cnf(c608,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),multiply(a,X2)) = multiply(greatest_lower_bound(a,multiply(multiply(a,b),a)),X2),
inference(symmetry,[status(thm)],[c607]) ).
cnf(c609,plain,
multiply(multiply(a,b),a) = multiply(a,multiply(b,a)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c610,plain,
greatest_lower_bound(a,multiply(multiply(a,b),a)) = greatest_lower_bound(a,multiply(a,multiply(b,a))),
inference(congruence,[status(thm)],[c609]) ).
cnf(c611,plain,
multiply(greatest_lower_bound(a,multiply(multiply(a,b),a)),X2) = multiply(greatest_lower_bound(a,multiply(a,multiply(b,a))),X2),
inference(congruence,[status(thm)],[c610]) ).
cnf(c612,plain,
multiply(greatest_lower_bound(a,multiply(a,multiply(b,a))),X2) = multiply(a,greatest_lower_bound(X2,multiply(multiply(b,a),X2))),
inference(substitution,[status(thm)],[c507]) ).
cnf(c613,plain,
multiply(greatest_lower_bound(X2,identity),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c19]) ).
cnf(c614,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,identity),X3)) = greatest_lower_bound(X3,greatest_lower_bound(X3,multiply(X2,X3))),
inference(congruence,[status(thm)],[c613]) ).
cnf(c615,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,X2)) = greatest_lower_bound(greatest_lower_bound(X3,X3),X2),
inference(substitution,[status(thm)],[c39]) ).
cnf(c616,axiom,
greatest_lower_bound(X2,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c617,plain,
greatest_lower_bound(greatest_lower_bound(X3,X3),X2) = greatest_lower_bound(X3,X2),
inference(congruence,[status(thm)],[c616]) ).
cnf(c618,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c615,c617]) ).
cnf(c619,plain,
greatest_lower_bound(X3,greatest_lower_bound(X3,multiply(X2,X3))) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(substitution,[status(thm)],[c618]) ).
cnf(c620,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,identity),X3)) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(transitivity,[status(thm)],[c614,c619]) ).
cnf(c621,plain,
greatest_lower_bound(X2,multiply(greatest_lower_bound(multiply(b,a),identity),X2)) = greatest_lower_bound(X2,multiply(multiply(b,a),X2)),
inference(substitution,[status(thm)],[c620]) ).
cnf(c622,plain,
greatest_lower_bound(X2,multiply(multiply(b,a),X2)) = greatest_lower_bound(X2,multiply(greatest_lower_bound(multiply(b,a),identity),X2)),
inference(symmetry,[status(thm)],[c621]) ).
cnf(c623,plain,
multiply(greatest_lower_bound(multiply(b,a),identity),X2) = multiply(greatest_lower_bound(multiply(a,b),identity),X2),
inference(congruence,[status(thm)],[c472]) ).
cnf(c624,plain,
greatest_lower_bound(X2,multiply(greatest_lower_bound(multiply(b,a),identity),X2)) = greatest_lower_bound(X2,multiply(greatest_lower_bound(multiply(a,b),identity),X2)),
inference(congruence,[status(thm)],[c623]) ).
cnf(c625,plain,
greatest_lower_bound(X2,multiply(greatest_lower_bound(multiply(a,b),identity),X2)) = greatest_lower_bound(X2,multiply(multiply(a,b),X2)),
inference(substitution,[status(thm)],[c620]) ).
cnf(c626,plain,
greatest_lower_bound(X2,multiply(greatest_lower_bound(multiply(b,a),identity),X2)) = greatest_lower_bound(X2,multiply(multiply(a,b),X2)),
inference(transitivity,[status(thm)],[c624,c625]) ).
cnf(c627,plain,
greatest_lower_bound(X2,multiply(multiply(b,a),X2)) = greatest_lower_bound(X2,multiply(multiply(a,b),X2)),
inference(transitivity,[status(thm)],[c622,c626]) ).
cnf(c628,plain,
multiply(a,greatest_lower_bound(X2,multiply(multiply(b,a),X2))) = multiply(a,greatest_lower_bound(X2,multiply(multiply(a,b),X2))),
inference(congruence,[status(thm)],[c627]) ).
cnf(c629,plain,
multiply(greatest_lower_bound(a,multiply(a,multiply(b,a))),X2) = multiply(a,greatest_lower_bound(X2,multiply(multiply(a,b),X2))),
inference(transitivity,[status(thm)],[c612,c628]) ).
cnf(c630,plain,
multiply(greatest_lower_bound(a,multiply(multiply(a,b),a)),X2) = multiply(a,greatest_lower_bound(X2,multiply(multiply(a,b),X2))),
inference(transitivity,[status(thm)],[c611,c629]) ).
cnf(c631,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),multiply(a,X2)) = multiply(a,greatest_lower_bound(X2,multiply(multiply(a,b),X2))),
inference(transitivity,[status(thm)],[c608,c630]) ).
cnf(c632,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),multiply(a,identity)) = multiply(a,greatest_lower_bound(identity,multiply(multiply(a,b),identity))),
inference(substitution,[status(thm)],[c631]) ).
cnf(c633,plain,
multiply(multiply(a,b),identity) = multiply(a,b),
inference(substitution,[status(thm)],[c95]) ).
cnf(c634,plain,
greatest_lower_bound(identity,multiply(multiply(a,b),identity)) = greatest_lower_bound(identity,multiply(a,b)),
inference(congruence,[status(thm)],[c633]) ).
cnf(c635,plain,
multiply(a,greatest_lower_bound(identity,multiply(multiply(a,b),identity))) = multiply(a,greatest_lower_bound(identity,multiply(a,b))),
inference(congruence,[status(thm)],[c634]) ).
cnf(c636,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c637,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(symmetry,[status(thm)],[c636]) ).
cnf(c638,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c637]) ).
cnf(c639,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c638,c527]) ).
cnf(c640,plain,
multiply(a,greatest_lower_bound(identity,multiply(a,b))) = greatest_lower_bound(a,multiply(a,multiply(a,b))),
inference(substitution,[status(thm)],[c639]) ).
cnf(c641,plain,
greatest_lower_bound(multiply(X2,b),multiply(X2,a)) = multiply(X2,greatest_lower_bound(a,b)),
inference(substitution,[status(thm)],[c406]) ).
cnf(c642,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(multiply(a,b),identity),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c643,plain,
multiply(X2,greatest_lower_bound(a,b)) = multiply(X2,greatest_lower_bound(multiply(a,b),identity)),
inference(congruence,[status(thm)],[c642]) ).
cnf(c644,plain,
multiply(X2,greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(X2,multiply(X2,multiply(a,b))),
inference(substitution,[status(thm)],[c527]) ).
cnf(c645,plain,
multiply(X2,greatest_lower_bound(a,b)) = greatest_lower_bound(X2,multiply(X2,multiply(a,b))),
inference(transitivity,[status(thm)],[c643,c644]) ).
cnf(c646,plain,
greatest_lower_bound(multiply(X2,b),multiply(X2,a)) = greatest_lower_bound(X2,multiply(X2,multiply(a,b))),
inference(transitivity,[status(thm)],[c641,c645]) ).
cnf(c647,plain,
greatest_lower_bound(multiply(a,b),multiply(a,a)) = greatest_lower_bound(a,multiply(a,multiply(a,b))),
inference(substitution,[status(thm)],[c646]) ).
cnf(c648,plain,
greatest_lower_bound(a,multiply(a,multiply(a,b))) = greatest_lower_bound(multiply(a,b),multiply(a,a)),
inference(symmetry,[status(thm)],[c647]) ).
cnf(c649,plain,
multiply(a,greatest_lower_bound(identity,multiply(a,b))) = greatest_lower_bound(multiply(a,b),multiply(a,a)),
inference(transitivity,[status(thm)],[c640,c648]) ).
cnf(c650,plain,
multiply(a,greatest_lower_bound(identity,multiply(multiply(a,b),identity))) = greatest_lower_bound(multiply(a,b),multiply(a,a)),
inference(transitivity,[status(thm)],[c635,c649]) ).
cnf(c651,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),multiply(a,identity)) = greatest_lower_bound(multiply(a,b),multiply(a,a)),
inference(transitivity,[status(thm)],[c632,c650]) ).
cnf(c652,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),a) = greatest_lower_bound(multiply(a,b),multiply(a,a)),
inference(transitivity,[status(thm)],[c601,c651]) ).
cnf(c653,plain,
greatest_lower_bound(a,multiply(multiply(a,b),a)) = greatest_lower_bound(multiply(a,b),multiply(a,a)),
inference(transitivity,[status(thm)],[c598,c652]) ).
cnf(c654,plain,
greatest_lower_bound(multiply(b,a),multiply(a,a)) = greatest_lower_bound(multiply(a,b),multiply(a,a)),
inference(transitivity,[status(thm)],[c596,c653]) ).
cnf(c655,plain,
multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(a,a))) = multiply(inverse(a),greatest_lower_bound(multiply(a,b),multiply(a,a))),
inference(congruence,[status(thm)],[c654]) ).
cnf(c656,plain,
greatest_lower_bound(X2,multiply(X4,X3)) = greatest_lower_bound(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c657,plain,
greatest_lower_bound(multiply(X4,X3),X2) = greatest_lower_bound(X2,multiply(X4,X3)),
inference(symmetry,[status(thm)],[c656]) ).
cnf(c658,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X3),X2)) = multiply(inverse(X4),greatest_lower_bound(X2,multiply(X4,X3))),
inference(congruence,[status(thm)],[c657]) ).
cnf(c659,plain,
multiply(inverse(X4),greatest_lower_bound(X2,multiply(X4,X3))) = greatest_lower_bound(X3,multiply(inverse(X4),X2)),
inference(substitution,[status(thm)],[c252]) ).
cnf(c660,plain,
multiply(inverse(X4),greatest_lower_bound(multiply(X4,X3),X2)) = greatest_lower_bound(X3,multiply(inverse(X4),X2)),
inference(transitivity,[status(thm)],[c658,c659]) ).
cnf(c661,plain,
multiply(inverse(a),greatest_lower_bound(multiply(a,b),multiply(a,a))) = greatest_lower_bound(b,multiply(inverse(a),multiply(a,a))),
inference(substitution,[status(thm)],[c660]) ).
cnf(c662,plain,
multiply(inverse(a),multiply(a,a)) = a,
inference(substitution,[status(thm)],[c27]) ).
cnf(c663,plain,
greatest_lower_bound(b,multiply(inverse(a),multiply(a,a))) = greatest_lower_bound(b,a),
inference(congruence,[status(thm)],[c662]) ).
cnf(c664,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(a,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c665,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(multiply(a,b),identity),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c666,plain,
greatest_lower_bound(b,a) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c664,c665]) ).
cnf(c667,plain,
greatest_lower_bound(b,multiply(inverse(a),multiply(a,a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c663,c666]) ).
cnf(c668,plain,
multiply(inverse(a),greatest_lower_bound(multiply(a,b),multiply(a,a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c661,c667]) ).
cnf(c669,plain,
multiply(inverse(a),greatest_lower_bound(multiply(b,a),multiply(a,a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c655,c668]) ).
cnf(c670,plain,
greatest_lower_bound(a,multiply(inverse(a),multiply(b,a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c589,c669]) ).
cnf(c671,plain,
greatest_lower_bound(multiply(a,b),identity) = greatest_lower_bound(a,multiply(inverse(a),multiply(b,a))),
inference(symmetry,[status(thm)],[c670]) ).
cnf(c672,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))) = multiply(greatest_lower_bound(a,multiply(inverse(a),multiply(b,a))),inverse(multiply(b,a))),
inference(congruence,[status(thm)],[c671]) ).
cnf(c673,plain,
greatest_lower_bound(multiply(X3,multiply(X2,inverse(X2))),multiply(X4,inverse(X2))) = multiply(greatest_lower_bound(X4,multiply(X3,X2)),inverse(X2)),
inference(substitution,[status(thm)],[c499]) ).
cnf(c674,plain,
multiply(greatest_lower_bound(X4,multiply(X3,X2)),inverse(X2)) = greatest_lower_bound(multiply(X3,multiply(X2,inverse(X2))),multiply(X4,inverse(X2))),
inference(symmetry,[status(thm)],[c673]) ).
cnf(c675,plain,
multiply(X3,multiply(X2,inverse(X2))) = multiply(X3,identity),
inference(congruence,[status(thm)],[c152]) ).
cnf(c676,plain,
greatest_lower_bound(multiply(X3,multiply(X2,inverse(X2))),multiply(X4,inverse(X2))) = greatest_lower_bound(multiply(X3,identity),multiply(X4,inverse(X2))),
inference(congruence,[status(thm)],[c675]) ).
cnf(c677,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X4,inverse(X2))) = greatest_lower_bound(X3,multiply(X4,inverse(X2))),
inference(congruence,[status(thm)],[c95]) ).
cnf(c678,plain,
greatest_lower_bound(multiply(X3,multiply(X2,inverse(X2))),multiply(X4,inverse(X2))) = greatest_lower_bound(X3,multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c676,c677]) ).
cnf(c679,plain,
multiply(greatest_lower_bound(X4,multiply(X3,X2)),inverse(X2)) = greatest_lower_bound(X3,multiply(X4,inverse(X2))),
inference(transitivity,[status(thm)],[c674,c678]) ).
cnf(c680,plain,
multiply(greatest_lower_bound(a,multiply(inverse(a),multiply(b,a))),inverse(multiply(b,a))) = greatest_lower_bound(inverse(a),multiply(a,inverse(multiply(b,a)))),
inference(substitution,[status(thm)],[c679]) ).
cnf(c681,plain,
multiply(a,inverse(multiply(b,a))) = inverse(b),
inference(substitution,[status(thm)],[c541]) ).
cnf(c682,plain,
greatest_lower_bound(inverse(a),multiply(a,inverse(multiply(b,a)))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(congruence,[status(thm)],[c681]) ).
cnf(c683,plain,
multiply(inverse(multiply(a,b)),identity) = inverse(multiply(a,b)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c684,plain,
inverse(multiply(a,b)) = multiply(inverse(multiply(a,b)),identity),
inference(symmetry,[status(thm)],[c683]) ).
cnf(c685,plain,
greatest_lower_bound(identity,inverse(multiply(a,b))) = greatest_lower_bound(identity,multiply(inverse(multiply(a,b)),identity)),
inference(congruence,[status(thm)],[c684]) ).
cnf(c686,plain,
multiply(inverse(multiply(a,b)),greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(identity,multiply(inverse(multiply(a,b)),identity)),
inference(substitution,[status(thm)],[c108]) ).
cnf(c687,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(a,b)),identity)) = multiply(inverse(multiply(a,b)),greatest_lower_bound(multiply(a,b),identity)),
inference(symmetry,[status(thm)],[c686]) ).
cnf(c688,plain,
greatest_lower_bound(multiply(multiply(a,b),inverse(a)),a) = greatest_lower_bound(a,multiply(multiply(a,b),inverse(a))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c689,plain,
greatest_lower_bound(a,multiply(multiply(a,b),inverse(a))) = greatest_lower_bound(multiply(multiply(a,b),inverse(a)),a),
inference(symmetry,[status(thm)],[c688]) ).
cnf(c690,plain,
multiply(a,identity) = a,
inference(substitution,[status(thm)],[c95]) ).
cnf(c691,plain,
a = multiply(a,identity),
inference(symmetry,[status(thm)],[c690]) ).
cnf(c692,plain,
greatest_lower_bound(multiply(multiply(a,b),inverse(a)),a) = greatest_lower_bound(multiply(multiply(a,b),inverse(a)),multiply(a,identity)),
inference(congruence,[status(thm)],[c691]) ).
cnf(c693,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c694,plain,
greatest_lower_bound(multiply(multiply(X5,X3),X2),multiply(X5,X4)) = greatest_lower_bound(multiply(X5,multiply(X3,X2)),multiply(X5,X4)),
inference(congruence,[status(thm)],[c693]) ).
cnf(c695,plain,
multiply(X5,greatest_lower_bound(multiply(X3,X2),X4)) = greatest_lower_bound(multiply(X5,multiply(X3,X2)),multiply(X5,X4)),
inference(substitution,[status(thm)],[c105]) ).
cnf(c696,plain,
greatest_lower_bound(multiply(X5,multiply(X3,X2)),multiply(X5,X4)) = multiply(X5,greatest_lower_bound(multiply(X3,X2),X4)),
inference(symmetry,[status(thm)],[c695]) ).
cnf(c697,plain,
greatest_lower_bound(multiply(X3,X2),X4) = greatest_lower_bound(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c698,plain,
multiply(X5,greatest_lower_bound(multiply(X3,X2),X4)) = multiply(X5,greatest_lower_bound(X4,multiply(X3,X2))),
inference(congruence,[status(thm)],[c697]) ).
cnf(c699,plain,
greatest_lower_bound(multiply(X5,multiply(X3,X2)),multiply(X5,X4)) = multiply(X5,greatest_lower_bound(X4,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c696,c698]) ).
cnf(c700,plain,
greatest_lower_bound(multiply(multiply(X5,X3),X2),multiply(X5,X4)) = multiply(X5,greatest_lower_bound(X4,multiply(X3,X2))),
inference(transitivity,[status(thm)],[c694,c699]) ).
cnf(c701,plain,
greatest_lower_bound(multiply(multiply(a,b),inverse(a)),multiply(a,identity)) = multiply(a,greatest_lower_bound(identity,multiply(b,inverse(a)))),
inference(substitution,[status(thm)],[c700]) ).
cnf(c702,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X3)) = greatest_lower_bound(multiply(X3,inverse(X3)),multiply(X2,inverse(X3))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c703,plain,
greatest_lower_bound(multiply(X3,inverse(X3)),multiply(X2,inverse(X3))) = greatest_lower_bound(identity,multiply(X2,inverse(X3))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c704,plain,
multiply(greatest_lower_bound(X3,X2),inverse(X3)) = greatest_lower_bound(identity,multiply(X2,inverse(X3))),
inference(transitivity,[status(thm)],[c702,c703]) ).
cnf(c705,plain,
multiply(greatest_lower_bound(a,b),inverse(a)) = greatest_lower_bound(identity,multiply(b,inverse(a))),
inference(substitution,[status(thm)],[c704]) ).
cnf(c706,plain,
greatest_lower_bound(identity,multiply(b,inverse(a))) = multiply(greatest_lower_bound(a,b),inverse(a)),
inference(symmetry,[status(thm)],[c705]) ).
cnf(c707,plain,
multiply(a,greatest_lower_bound(identity,multiply(b,inverse(a)))) = multiply(a,multiply(greatest_lower_bound(a,b),inverse(a))),
inference(congruence,[status(thm)],[c706]) ).
cnf(c708,plain,
multiply(greatest_lower_bound(multiply(a,b),multiply(a,a)),inverse(a)) = multiply(a,multiply(greatest_lower_bound(a,b),inverse(a))),
inference(substitution,[status(thm)],[c482]) ).
cnf(c709,plain,
multiply(a,multiply(greatest_lower_bound(a,b),inverse(a))) = multiply(greatest_lower_bound(multiply(a,b),multiply(a,a)),inverse(a)),
inference(symmetry,[status(thm)],[c708]) ).
cnf(c710,plain,
greatest_lower_bound(multiply(a,b),multiply(a,a)) = greatest_lower_bound(multiply(b,a),multiply(a,a)),
inference(symmetry,[status(thm)],[c654]) ).
cnf(c711,plain,
multiply(greatest_lower_bound(multiply(a,b),multiply(a,a)),inverse(a)) = multiply(greatest_lower_bound(multiply(b,a),multiply(a,a)),inverse(a)),
inference(congruence,[status(thm)],[c710]) ).
cnf(c712,plain,
multiply(greatest_lower_bound(multiply(b,a),multiply(a,a)),inverse(a)) = greatest_lower_bound(a,multiply(multiply(b,a),inverse(a))),
inference(substitution,[status(thm)],[c679]) ).
cnf(c713,plain,
multiply(multiply(X3,X2),inverse(X2)) = multiply(X3,multiply(X2,inverse(X2))),
inference(substitution,[status(thm)],[c22]) ).
cnf(c714,plain,
multiply(X3,multiply(X2,inverse(X2))) = multiply(X3,identity),
inference(congruence,[status(thm)],[c152]) ).
cnf(c715,plain,
multiply(X3,multiply(X2,inverse(X2))) = X3,
inference(transitivity,[status(thm)],[c714,c95]) ).
cnf(c716,plain,
multiply(multiply(X3,X2),inverse(X2)) = X3,
inference(transitivity,[status(thm)],[c713,c715]) ).
cnf(c717,plain,
multiply(multiply(b,a),inverse(a)) = b,
inference(substitution,[status(thm)],[c716]) ).
cnf(c718,plain,
greatest_lower_bound(a,multiply(multiply(b,a),inverse(a))) = greatest_lower_bound(a,b),
inference(congruence,[status(thm)],[c717]) ).
cnf(c719,plain,
greatest_lower_bound(a,b) = greatest_lower_bound(multiply(a,b),identity),
inference(symmetry,[status(thm)],[c321]) ).
cnf(c720,plain,
greatest_lower_bound(a,multiply(multiply(b,a),inverse(a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c718,c719]) ).
cnf(c721,plain,
multiply(greatest_lower_bound(multiply(b,a),multiply(a,a)),inverse(a)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c712,c720]) ).
cnf(c722,plain,
multiply(greatest_lower_bound(multiply(a,b),multiply(a,a)),inverse(a)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c711,c721]) ).
cnf(c723,plain,
multiply(a,multiply(greatest_lower_bound(a,b),inverse(a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c709,c722]) ).
cnf(c724,plain,
multiply(a,greatest_lower_bound(identity,multiply(b,inverse(a)))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c707,c723]) ).
cnf(c725,plain,
greatest_lower_bound(multiply(multiply(a,b),inverse(a)),multiply(a,identity)) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c701,c724]) ).
cnf(c726,plain,
greatest_lower_bound(multiply(multiply(a,b),inverse(a)),a) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c692,c725]) ).
cnf(c727,plain,
greatest_lower_bound(a,multiply(multiply(a,b),inverse(a))) = greatest_lower_bound(multiply(a,b),identity),
inference(transitivity,[status(thm)],[c689,c726]) ).
cnf(c728,plain,
greatest_lower_bound(multiply(a,b),identity) = greatest_lower_bound(a,multiply(multiply(a,b),inverse(a))),
inference(symmetry,[status(thm)],[c727]) ).
cnf(c729,plain,
multiply(inverse(multiply(a,b)),greatest_lower_bound(multiply(a,b),identity)) = multiply(inverse(multiply(a,b)),greatest_lower_bound(a,multiply(multiply(a,b),inverse(a)))),
inference(congruence,[status(thm)],[c728]) ).
cnf(c730,plain,
multiply(inverse(multiply(a,b)),greatest_lower_bound(a,multiply(multiply(a,b),inverse(a)))) = greatest_lower_bound(inverse(a),multiply(inverse(multiply(a,b)),a)),
inference(substitution,[status(thm)],[c252]) ).
cnf(c731,plain,
X3 = multiply(multiply(X3,X2),inverse(X2)),
inference(symmetry,[status(thm)],[c716]) ).
cnf(c732,plain,
multiply(inverse(multiply(X3,X2)),X3) = multiply(inverse(multiply(X3,X2)),multiply(multiply(X3,X2),inverse(X2))),
inference(congruence,[status(thm)],[c731]) ).
cnf(c733,plain,
multiply(inverse(multiply(X3,X2)),multiply(multiply(X3,X2),inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c27]) ).
cnf(c734,plain,
multiply(inverse(multiply(X3,X2)),X3) = inverse(X2),
inference(transitivity,[status(thm)],[c732,c733]) ).
cnf(c735,plain,
multiply(inverse(multiply(a,b)),a) = inverse(b),
inference(substitution,[status(thm)],[c734]) ).
cnf(c736,plain,
greatest_lower_bound(inverse(a),multiply(inverse(multiply(a,b)),a)) = greatest_lower_bound(inverse(a),inverse(b)),
inference(congruence,[status(thm)],[c735]) ).
cnf(c737,plain,
multiply(inverse(multiply(a,b)),greatest_lower_bound(a,multiply(multiply(a,b),inverse(a)))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(transitivity,[status(thm)],[c730,c736]) ).
cnf(c738,plain,
multiply(inverse(multiply(a,b)),greatest_lower_bound(multiply(a,b),identity)) = greatest_lower_bound(inverse(a),inverse(b)),
inference(transitivity,[status(thm)],[c729,c737]) ).
cnf(c739,plain,
greatest_lower_bound(identity,multiply(inverse(multiply(a,b)),identity)) = greatest_lower_bound(inverse(a),inverse(b)),
inference(transitivity,[status(thm)],[c687,c738]) ).
cnf(c740,plain,
greatest_lower_bound(identity,inverse(multiply(a,b))) = greatest_lower_bound(inverse(a),inverse(b)),
inference(transitivity,[status(thm)],[c685,c739]) ).
cnf(c741,plain,
greatest_lower_bound(inverse(a),inverse(b)) = greatest_lower_bound(identity,inverse(multiply(a,b))),
inference(symmetry,[status(thm)],[c740]) ).
cnf(c742,plain,
greatest_lower_bound(inverse(a),multiply(a,inverse(multiply(b,a)))) = greatest_lower_bound(identity,inverse(multiply(a,b))),
inference(transitivity,[status(thm)],[c682,c741]) ).
cnf(c743,plain,
multiply(greatest_lower_bound(a,multiply(inverse(a),multiply(b,a))),inverse(multiply(b,a))) = greatest_lower_bound(identity,inverse(multiply(a,b))),
inference(transitivity,[status(thm)],[c680,c742]) ).
cnf(c744,plain,
multiply(greatest_lower_bound(multiply(a,b),identity),inverse(multiply(b,a))) = greatest_lower_bound(identity,inverse(multiply(a,b))),
inference(transitivity,[status(thm)],[c672,c743]) ).
cnf(c745,plain,
greatest_lower_bound(inverse(multiply(b,a)),multiply(multiply(a,b),inverse(multiply(b,a)))) = greatest_lower_bound(identity,inverse(multiply(a,b))),
inference(transitivity,[status(thm)],[c587,c744]) ).
cnf(c746,plain,
greatest_lower_bound(identity,inverse(multiply(b,a))) = greatest_lower_bound(identity,inverse(multiply(a,b))),
inference(transitivity,[status(thm)],[c585,c745]) ).
cnf(c747,plain,
inverse(greatest_lower_bound(identity,inverse(multiply(b,a)))) = inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),
inference(congruence,[status(thm)],[c746]) ).
cnf(c748,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(b,a)))),greatest_lower_bound(multiply(b,a),identity)) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),greatest_lower_bound(multiply(b,a),identity)),
inference(congruence,[status(thm)],[c747]) ).
cnf(c749,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),greatest_lower_bound(multiply(b,a),identity)) = multiply(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),greatest_lower_bound(multiply(a,b),identity)),
inference(congruence,[status(thm)],[c472]) ).
cnf(c750,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),greatest_lower_bound(multiply(a,b),identity)) = multiply(a,b),
inference(substitution,[status(thm)],[c32]) ).
cnf(c751,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(a,b)))),greatest_lower_bound(multiply(b,a),identity)) = multiply(a,b),
inference(transitivity,[status(thm)],[c749,c750]) ).
cnf(c752,plain,
multiply(inverse(greatest_lower_bound(identity,inverse(multiply(b,a)))),greatest_lower_bound(multiply(b,a),identity)) = multiply(a,b),
inference(transitivity,[status(thm)],[c748,c751]) ).
cnf(c753,plain,
multiply(b,a) = multiply(a,b),
inference(transitivity,[status(thm)],[c34,c752]) ).
cnf(c754,plain,
multiply(a,b) = multiply(b,a),
inference(symmetry,[status(thm)],[c753]) ).
cnf(c755,plain,
$false,
inference(resolution,[status(thm)],[c1,c754]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP187-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:39:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 102.81/13.43 Command-line arguments: --flatten-regeneralise
% 102.81/13.43
% 102.81/13.43 % SZS status Unsatisfiable
% 102.81/13.43
% 102.81/13.48 % SZS output start CNFRefutation
% See solution above
% 105.99/13.82
% 105.99/13.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------